Davide Ferrario writes:
Dear Gap Forum,
I would like to know whether GAP can be (or has been) used in algebraic
topology, and in which areas, if someone has already done something.
For example, Lambda-algebras, spectral sequences, homotopy groups of
spheres, effective homology, fixed/periodic points and so on.
I appreciate any kind of info/help.
Thank you in advance,
Sarah Rees and I have developed algorithms to compute in 2-dimensional
combinatorial cell complexes, and these algorithms have been
implemented in GAP3/GRAPE for clique complexes of finite graphs. Given
such a complex, these programs (available from me) can compute the
fundamental group, abelianized fundamental group, and abelianized
fundamental group mod a prime, with increasing levels of efficiency.
The programs can also compute covers and deck groups. An article
explaining our approach and algorithms will appear in the Journal of