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132 publications using GAP in the category "Manifolds and cell complexes"

[ABL17] Adiprasito, K. A., Benedetti, B., and Lutz, F. H., Extremal examples of collapsible complexes and random discrete Morse theory, Discrete Comput. Geom., 57 (4) (2017), 824–853.

[AP08] Akhmedov, A. and Park, B. D., Exotic smooth structures on small 4-manifolds, Invent. Math., 173 (1) (2008), 209–223.

[AEJ19] Aldwaik, S., Edjvet, M., and Juh\'asz, A., Asphericity of positive free product length 4 relative group presentations, Forum Math., 31 (1) (2019), 49–68.

[AH10] Allcock, D. and Hall, C., Monodromy groups of Hurwitz-type problems, Adv. Math., 225 (1) (2010), 69–80.

[A01] Alp, M., Induced $\rm cat^1$-groups, Turkish J. Math., 25 (2) (2001), 245–261.

[AW12] Anderson, J. W. and Wootton, A., A lower bound for the number of group actions on a compact Riemann surface, Algebr. Geom. Topol., 12 (1) (2012), 19–35.

[A97] Artal Bartolo, E., A curve of degree five with non-abelian fundamental group, Topology Appl., 79 (1) (1997), 13–29.

[AC+05] Artal Bartolo, E., Carmona Ruber, J., Cogolludo-Agust\'in, J. I., and Marco Buzun\'ariz, M., Topology and combinatorics of real line arrangements, Compos. Math., 141 (6) (2005), 1578–1588.

[ACO14] Artal Bartolo, E., Cogolludo-Agust\'in, J. I., and Ortigas-Galindo, J., Kummer covers and braid monodromy, J. Inst. Math. Jussieu, 13 (3) (2014), 633–670.

[A07] Asaeda, M., Galois groups and an obstruction to principal graphs of subfactors, Internat. J. Math., 18 (2) (2007), 191–202.

[BD12] Bagchi, B. and Datta, B., A triangulation of $\Bbb CP^3$ as symmetric cube of $S^2$, Discrete Comput. Geom., 48 (2) (2012), 310–329.

[B01] Baker, M. D., Link complements and the Bianchi modular groups, Trans. Amer. Math. Soc., 353 (8) (2001), 3229–3246.

[BGR19] Baker, M. D., Goerner, M., and Reid, A. W., All principal congruence link groups, J. Algebra, 528 (2019), 497–504.

[BV03] Bardakov, V. G. and Vesnin, A. Y., On a generalization of Fibonacci groups, Algebra Logika, 42 (2) (2003), 131–160, 255.

[BD17] Bartholdi, L. and Dudko, D., Algorithmic aspects of branched coverings, Ann. Fac. Sci. Toulouse Math. (6), 26 (5) (2017), 1219–1296.

[BS04] Bennett, C. D. and Shpectorov, S., A new proof of a theorem of Phan, J. Group Theory, 7 (3) (2004), 287–310.

[B05] Bessis, D., Variations on Van Kampen's method, J. Math. Sci. (N.Y.), 128 (4) (2005), 3142–3150
(Geometry).

[B03] Bessis, D., The dual braid monoid, Ann. Sci. École Norm. Sup. (4), 36 (5) (2003), 647–683.

[BAE17] Bin Ahmad, A. G., Al-Mulla, M. A., and Edjvet, M., Asphericity of a length four relative group presentation, J. Algebra Appl., 16 (4) (2017), 1750076, 27.

[BL00] Björner, A. and Lutz, F. H., Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincaré homology 3-sphere, Experiment. Math., 9 (2) (2000), 275–289.

[BW16] Bogley, W. A. and Williams, G., Efficient finite groups arising in the study of relative asphericity, Math. Z., 284 (1-2) (2016), 507–535.

[BD+15] Brendel, P., Dłotko, P., Ellis, G., Juda, M., and Mrozek, M., Computing fundamental groups from point clouds, Appl. Algebra Engrg. Comm. Comput., 26 (1-2) (2015), 27–48.

[BHT13] Brittenham, M., Hermiller, S., and Todd, R. G., 4-moves and the Dabkowski-Sahi invariant for knots, J. Knot Theory Ramifications, 22 (11) (2013), 1350069, 20.

[BW07] Broughton, S. A. and Wootton, A., Finite abelian subgroups of the mapping class group, Algebr. Geom. Topol., 7 (2007), 1651–1697.

[BW03] Brown, R. and Wensley, C. D., Computation and homotopical applications of induced crossed modules, J. Symbolic Comput., 35 (1) (2003), 59–72.

[B18] Bulai, L., Unlinking numbers of links with crossing number 10, Involve, 11 (2) (2018), 335–353.

[CD06] Calegari, F. and Dunfield, N. M., Automorphic forms and rational homology 3-spheres, Geom. Topol., 10 (2006), 295–329.

[CDW99] Callahan, P. J., Dean, J. C., and Weeks, J. R., The simplest hyperbolic knots, J. Knot Theory Ramifications, 8 (3) (1999), 279–297.

[CT16] Caroli, M. and Teillaud, M., Delaunay triangulations of closed Euclidean $d$-orbifolds, Discrete Comput. Geom., 55 (4) (2016), 827–853.

[CC08] Casali, M. R. and Cristofori, P., A catalogue of orientable 3-manifolds triangulated by 30 colored tetrahedra, J. Knot Theory Ramifications, 17 (5) (2008), 579–599.

[CC+11] Catalano, D. A., Conder, M. D. E., Du, S. F., Kwon, Y. S., Nedela, R., and Wilson, S., Classification of regular embeddings of $n$-dimensional cubes, J. Algebraic Combin., 33 (2) (2011), 215–238.

[CE+13] Clark, W. E., Elhamdadi, M., Hou, X., Saito, M., and Yeatman, T., Connected quandles associated with pointed abelian groups, Pacific J. Math., 264 (1) (2013), 31–60.

[CE+14] Clark, W. E., Elhamdadi, M., Saito, M., and Yeatman, T., Quandle colorings of knots and applications, J. Knot Theory Ramifications, 23 (6) (2014), 1450035, 29.

[C94] Conder, M., Regular maps with small parameters, J. Austral. Math. Soc. Ser. A, 57 (1) (1994), 103–112.

[CM+03] Conder, M., Maclachlan, C., Todorovic Vasiljevic, S., and Wilson, S., Bounds for the number of automorphisms of a compact non-orientable surface, J. London Math. Soc. (2), 68 (1) (2003), 65–82.

[CH95] Conway, J. H. and Hsu, T., Quilts and $T$-systems, J. Algebra, 174 (3) (1995), 856–908.

[CM16] Cristofori, P. and Mulazzani, M., Compact 3-manifolds via 4-colored graphs, Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. RACSAM, 110 (2) (2016), 395–416.

[CL06] Csorba, P. and Lutz, F. H., Graph coloring manifolds, in Algebraic and geometric combinatorics, Amer. Math. Soc., Providence, RI, Contemp. Math., 423 (2006), 51–69.

[DJ+11] Dabkowski, M. K., Jablan, S., Khan, N. A., and Sahi, R. K., On 4-move equivalence classes of knots and links of two components, J. Knot Theory Ramifications, 20 (1) (2011), 47–90.

[DS13] Datta, B. and Singh, N., An infinite family of tight triangulations of manifolds, J. Combin. Theory Ser. A, 120 (8) (2013), 2148–2163.

[DE02] Dekimpe, K. and Eick, B., Computational aspects of group extensions and their applications in topology, Experiment. Math., 11 (2) (2002), 183–200.

[DIM01] Dekimpe, K., Igodt, P., and Malfait, W., Infra-nilmanifolds and their fundamental groups, J. Korean Math. Soc., 38 (5) (2001), 883–914
(Mathematics in the new millennium (Seoul, 2000)).

[DT03] Dunfield, N. M. and Thurston, W. P., The virtual Haken conjecture: experiments and examples, Geom. Topol., 7 (2003), 399–441.

[E11] Effenberger, F., Stacked polytopes and tight triangulations of manifolds, J. Combin. Theory Ser. A, 118 (6) (2011), 1843–1862.

[E07] Eisermann, M., Knot colouring polynomials, Pacific J. Math., 231 (2) (2007), 305–336.

[E00] Eisermann, M., Knotengruppen-Darstellungen und Invarianten von endlichem Typ, Universität Bonn, Mathematisches Institut, Bonn, Bonner Mathematische Schriften [Bonn Mathematical Publications], 327 (2000), viii+135 pages
(Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, 2000).

[EMM03] Elder, M., McCammond, J., and Meier, J., Combinatorial conditions that imply word-hyperbolicity for 3-manifolds, Topology, 42 (6) (2003), 1241–1259.

[E04] Ellis, G., Computing group resolutions, J. Symbolic Comput., 38 (3) (2004), 1077–1118.

[EF18] Ellis, G. and Fragnaud, C., Computing with knot quandles, J. Knot Theory Ramifications, 27 (14) (2018), 1850074, 18.

[EH14] Ellis, G. and Hegarty, F., Computational homotopy of finite regular CW-spaces, J. Homotopy Relat. Struct., 9 (1) (2014), 25–54.

[EM10] Ellis, G. and Mikhailov, R., A colimit of classifying spaces, Adv. Math., 223 (6) (2010), 2097–2113.

[EW05] Ellis, G. and Williams, G., On the cohomology of generalized triangle groups, Comment. Math. Helv., 80 (3) (2005), 571–591.

[FG16] Farinati, M. A. and Garc\'ia Galofre, J., Link and knot invariants from non-abelian Yang-Baxter 2-cocycles, J. Knot Theory Ramifications, 25 (13) (2016), 1650070, 29.

[FG19] Farinati, M. A. and Garc\'ia Galofre, J., Virtual link and knot invariants from non-abelian Yang-Baxter 2-cocycle pairs, Osaka J. Math., 56 (3) (2019), 525–547.

[F00] Ferrario, D. L., Equivariant deformations of manifolds and real representations, Pacific J. Math., 196 (2) (2000), 353–368.

[F14] Francis, A. R., An algebraic view of bacterial genome evolution, J. Math. Biol., 69 (6-7) (2014), 1693–1718.

[FG14] Friedman, M. and Garber, D., On the structure of fundamental groups of conic-line arrangements having a cycle in their graph, Topology Appl., 177 (2014), 34–58.

[G16] Gobet, T., Noncrossing partitions, fully commutative elements and bases of the Temperley-Lieb algebra, J. Knot Theory Ramifications, 25 (6) (2016), 1650035, 27.

[G19] Gorodkov, D., A 15-vertex triangulation of the quaternionic projective plane, Discrete Comput. Geom., 62 (2) (2019), 348–373.

[H10] Harris, J. M., The Kauffman bracket skein module of surgery on a $(2,2b)$ torus link, Pacific J. Math., 245 (1) (2010), 119–140.

[HLM99] Hilden, H. M., Lozano, M. T., and Montesinos-Amilibia, J. M., The Chern-Simons invariants of hyperbolic manifolds via covering spaces, Bull. London Math. Soc., 31 (3) (1999), 354–366.

[HS08] Hiss, G. and Szczepa\'nski, A., Spin structures on flat manifolds with cyclic holonomy, Comm. Algebra, 36 (1) (2008), 11–22.

[HS95] Hiss, G. and Szczepa\'nski, A., Holonomy groups of Bieberbach groups with finite outer automorphism groups, Arch. Math. (Basel), 65 (1) (1995), 8–14.

[HRW08] Hong, S., Rowell, E., and Wang, Z., On exotic modular tensor categories, Commun. Contemp. Math., 10 (suppl. 1) (2008), 1049–1074.

[HW06] Howie, J. and Williams, G., Free subgroups in certain generalized triangle groups of type $(2,m,2)$, Geom. Dedicata, 119 (2006), 181–197.

[HW12] Howie, J. and Williams, G., Tadpole labelled oriented graph groups and cyclically presented groups, J. Algebra, 371 (2012), 521–535.

[HSV16] Hulpke, A., Stanovsk\'y, D., and Vojt\vechovsk\'y, P., Connected quandles and transitive groups, J. Pure Appl. Algebra, 220 (2) (2016), 735–758.

[IM10] Idalʹgo, R. A. and Mednykh, A. D., Geometric orbifolds with a torsion-free derived group, Sibirsk. Mat. Zh., 51 (1) (2010), 48–61.

[JP+15] Jedli\vcka, P., Pilitowska, A., Stanovsk\'y, D., and Zamojska-Dzienio, A., The structure of medial quandles, J. Algebra, 443 (2015), 300–334.

[J10] Ju, X., The Smith set of the group $S_5 \times C_2 \times \dots \times C_2$, Osaka J. Math., 47 (1) (2010), 215–236.

[KO14] Kalliongis, J. and Ohashi, R., Classifying non-splitting fiber preserving actions on prism manifolds, Topology Appl., 178 (2014), 200–218.

[KS19] Kanenobu, T. and Sumi, T., Classification of ribbon 2-knots presented by virtual arcs with up to four crossings, J. Knot Theory Ramifications, 28 (10) (2019), 1950067, 18.

[KMN07] Karab\'a\vs, J., Mali\vck\'y, P., and Nedela, R., Three-manifolds with Heegaard genus at most two represented by crystallisations with at most 42 vertices, Discrete Math., 307 (21) (2007), 2569–2590.

[KL99] Kühnel, W. and Lutz, F. H., A census of tight triangulations, Period. Math. Hungar., 39 (1-3) (1999), 161–183
(Discrete geometry and rigidity (Budapest, 1999)).

[KR08] Kim, H. J. and Ruberman, D., Topological triviality of smoothly knotted surfaces in 4-manifolds, Trans. Amer. Math. Soc., 360 (11) (2008), 5869–5881.

[K11] Korepanov, I. G., Relations in Grassmann algebra corresponding to three- and four-dimensional Pachner moves, SIGMA Symmetry Integrability Geom. Methods Appl., 7 (2011), Paper 117, 23.

[KMQ08] Koto, A., Morimoto, M., and Qi, Y., The Smith sets of finite groups with normal Sylow 2-subgroups and small nilquotients, J. Math. Kyoto Univ., 48 (1) (2008), 219–227.

[KO08] Kwak, J. H. and Oh, J., Arc-transitive elementary abelian covers of the octahedron graph, Linear Algebra Appl., 429 (8-9) (2008), 2180–2198.

[LNP03] Larri\'on, F., Neumann-Lara, V., and Piza\~na, M. A., Clique convergent surface triangulations, Mat. Contemp., 25 (2003), 135–143
(The Latin-American Workshop on Cliques in Graphs (Rio de Janeiro, 2002)).

[LS97] Leary, I. J. and Schuster, B., On the $\rm GL(V)$-module structure of $K(n)^*(BV)$, Math. Proc. Cambridge Philos. Soc., 122 (1) (1997), 73–89.

[L08] Long, C., Small volume closed hyperbolic 4-manifolds, Bull. Lond. Math. Soc., 40 (5) (2008), 913–916.

[L09] Lutowski, R., On symmetry of flat manifolds, Experiment. Math., 18 (2) (2009), 201–204.

[L08] Lutz, F. H., Combinatorial 3-manifolds with 10 vertices, Beiträge Algebra Geom., 49 (1) (2008), 97–106.

[L99] Lutz, F. H., Triangulated manifolds with few vertices and vertex-transitive group actions, Verlag Shaker, Aachen, Berichte aus der Mathematik. [Reports from Mathematics] (1999), vi+137 pages
(Dissertation, Technischen Universität Berlin, Berlin, 1999).

[MSV03] Magaard, K., Shpectorov, S., and Völklein, H., A GAP package for braid orbit computation and applications, Experiment. Math., 12 (4) (2003), 385–393.

[MP06] Malni\vc, A. and Poto\vcnik, P., Invariant subspaces, duality, and covers of the Petersen graph, European J. Combin., 27 (6) (2006), 971–989.

[MZ01] May, C. L. and Zimmerman, J., The group of symmetric Euler characteristic $-3$, Houston J. Math., 27 (4) (2001), 737–752.

[MS19] Müller, J. and Sarkar, S., A structured description of the genus spectrum of Abelian $p$-groups, Glasg. Math. J., 61 (2) (2019), 381–423.

[M10] Morimoto, M., Nontrivial $\scr P(G)$-matched $\germ S$-related pairs for finite gap Oliver groups, J. Math. Soc. Japan, 62 (2) (2010), 623–647.

[M08] Morimoto, M., Smith equivalent $\rm Aut(A_6)$-representations are isomorphic, Proc. Amer. Math. Soc., 136 (10) (2008), 3683–3688.

[NO15] Nagel, M. and Owens, B., Unlinking information from 4-manifolds, Bull. Lond. Math. Soc., 47 (6) (2015), 964–979.

[N01] Newman, M. F., On a family of cyclically-presented fundamental groups, J. Aust. Math. Soc., 71 (2) (2001), 235–241
(Special issue on group theory).

[N06] Niebrzydowski, M., On colored quandle longitudes and its applications to tangle embeddings and virtual knots, J. Knot Theory Ramifications, 15 (8) (2006), 1049–1059.

[N10] Niebrzydowski, M., Coloring invariants of spatial graphs, J. Knot Theory Ramifications, 19 (6) (2010), 829–841.

[NP06] Niebrzydowski, M. and Przytycki, J. H., Burnside kei, Fund. Math., 190 (2006), 211–229.

[NP09] Niebrzydowski, M. and Przytycki, J. H., Homology of dihedral quandles, J. Pure Appl. Algebra, 213 (5) (2009), 742–755.

[NP10] Niebrzydowski, M. and Przytycki, J. H., Homology operations on homology of quandles, J. Algebra, 324 (7) (2010), 1529–1548.

[NP11] Niebrzydowski, M. and Przytycki, J. H., The second quandle homology of the Takasaki quandle of an odd abelian group is an exterior square of the group, J. Knot Theory Ramifications, 20 (1) (2011), 171–177.

[NP13] Niebrzydowski, M. and Przytycki, J. H., Entropic magmas, their homology and related invariants of links and graphs, Algebr. Geom. Topol., 13 (6) (2013), 3223–3243.

[NO02] Nikkuni, R. and Onda, K., A characterization of knots in a spatial graph. II, J. Knot Theory Ramifications, 11 (7) (2002), 1133–1154.

[NR04] N\'u\~nez, V. and Rodr\'iguez-Viorato, J., Dihedral coverings of Montesinos knots, Bol. Soc. Mat. Mexicana (3), 10 (Special Issue) (2004), 423–449.

[PS06] Papadima, S. and Suciu, A. I., Algebraic invariants for right-angled Artin groups, Math. Ann., 334 (3) (2006), 533–555.

[PS13] Pawałowski, K. and Sumi, T., The Laitinen conjecture for finite non-solvable groups, Proc. Edinb. Math. Soc. (2), 56 (1) (2013), 303–336.

[PS09] Pawałowski, K. and Sumi, T., The Laitinen conjecture for finite solvable Oliver groups, Proc. Amer. Math. Soc., 137 (6) (2009), 2147–2156.

[PH18] Pedersen, M. C. and Hyde, S. T., Polyhedra and packings from hyperbolic honeycombs, Proc. Natl. Acad. Sci. USA, 115 (27) (2018), 6905–6910.

[P14] Pellicer, D., Vertex-transitive maps with Schläfli type $\3,7\$, Discrete Math., 317 (2014), 53–74.

[PS+13] Pellikka, M., Suuriniemi, S., Kettunen, L., and Geuzaine, C., Homology and cohomology computation in finite element modeling, SIAM J. Sci. Comput., 35 (5) (2013), B1195–B1214.

[P07] Putrycz, B., Commutator subgroups of Hantzsche-Wendt groups, J. Group Theory, 10 (3) (2007), 401–409.

[PS10] Putrycz, B. and Szczepa\'nski, A., Existence of spin structures on flat four-manifolds, Adv. Geom., 10 (2) (2010), 323–332.

[R07] Rattaggi, D., A finitely presented torsion-free simple group, J. Group Theory, 10 (3) (2007), 363–371.

[RS00] Rees, S. and Soicher, L. H., An algorithmic approach to fundamental groups and covers of combinatorial cell complexes, J. Symbolic Comput., 29 (1) (2000), 59–77.

[R01] Ruberman, D., Isospectrality and 3-manifold groups, Proc. Amer. Math. Soc., 129 (8) (2001), 2467–2471.

[S17] Sadofschi Costa, I., Presentation complexes with the fixed point property, Geom. Topol., 21 (2) (2017), 1275–1283.

[S15] Singh, N., Strongly minimal triangulations of $(S^3 \times S^1)^\#3$ and $(S^3\mathbin \times \kern-.7em_- \,S^1)^\#3$, Proc. Indian Acad. Sci. Math. Sci., 125 (1) (2015), 79–102.

[S11] Spreer, J., Normal surfaces as combinatorial slicings, Discrete Math., 311 (14) (2011), 1295–1309.

[S12] Spreer, J., Partitioning the triangles of the cross polytope into surfaces, Beitr. Algebra Geom., 53 (2) (2012), 473–486.

[S14] Spreer, J., Combinatorial 3-manifolds with transitive cyclic symmetry, Discrete Comput. Geom., 51 (2) (2014), 394–426.

[SK11] Spreer, J. and Kühnel, W., Combinatorial properties of the $K3$ surface: simplicial blowups and slicings, Exp. Math., 20 (2) (2011), 201–216.

[S10] Stoimenow, A., Tabulating and distinguishing mutants, Internat. J. Algebra Comput., 20 (4) (2010), 525–559.

[ST09] Stoimenow, A. and Tanaka, T., Mutation and the colored Jones polynomial, J. Gökova Geom. Topol. GGT, 3 (2009), 44–78.

[SV19] Stuhl, I. and Vojt\vechovsk\'y, P., Enumeration of involutory Latin quandles, Bruck loops and commutative automorphic loops of odd prime power order, in Nonassociative mathematics and its applications, Amer. Math. Soc., Providence, RI, Contemp. Math., 721 (2019), 261–276.

[S01] Suciu, A. I., Fundamental groups of line arrangements: enumerative aspects, in Advances in algebraic geometry motivated by physics (Lowell, MA, 2000), Amer. Math. Soc., Providence, RI, Contemp. Math., 276 (2001), 43–79.

[S18] Szczepa\'nski, A., Intersection forms of almost-flat 4-manifolds, Arch. Math. (Basel), 110 (5) (2018), 455–458.

[T00] Taherkhani, F., The Kazhdan property of the mapping class group of closed surfaces and the first cohomology group of its cofinite subgroups, Experiment. Math., 9 (2) (2000), 261–274.

[UTM14] Upadhyay, A. K., Tiwari, A. K., and Maity, D., Semi-equivelar maps, Beitr. Algebra Geom., 55 (1) (2014), 229–242.

[V12] Vendramin, L., On the classification of quandles of low order, J. Knot Theory Ramifications, 21 (9) (2012), 1250088, 10.

[VY19] Vojt\vechovsk\'y, P. and Yang, S. Y., Enumeration of racks and quandles up to isomorphism, Math. Comp., 88 (319) (2019), 2523–2540.

[W03] Waldmüller, R., A flat manifold with no symmetries, Experiment. Math., 12 (1) (2003), 71–77.

[WW+18] Wang, C., Wang, S., Zhang, Y., and Zimmermann, B., Graphs in the 3-sphere with maximum symmetry, Discrete Comput. Geom., 59 (2) (2018), 331–362.

[WW+18] Wang, C., Wang, S., Zhang, Y., and Zimmermann, B., Bordered surfaces in the 3-sphere with maximum symmetry, J. Pure Appl. Algebra, 222 (9) (2018), 2490–2504.

[WW+15] Wang, C., Wang, S., Zhang, Y., and Zimmermann, B., Embedding surfaces into $S^3$ with maximum symmetry, Groups Geom. Dyn., 9 (4) (2015), 1001–1045.

[WB04] Wilson, S. and Breda d'Azevedo, A., Surfaces having no regular hypermaps, Discrete Math., 277 (1-3) (2004), 241–274.