> < ^ Date: Mon, 07 Feb 2000 11:59:14 GMT
< ^ From: Volkmar Welker <welker@immd1.informatik.uni-erlangen.de >
< ^ Subject: Re: homology of subspace arrangements

Dear Forum,

The message below was posted by Volkmar Welker on January 21.
We apologize to him and to the other members of the forum for
the delay in sending it on.

Willem de Graaf


Franck Harou wrote:

Dear forum,

Does anyone know some method to compute the homology groups of subspace
arrangements (complement in C^n of subspace arrangement) ?


Franck Harou

Dear Franck Harou,

in the GAP forum you ask about the homology of the complement of a
susbapce arrangement in C^n. The Formula of Geresky-MacPherson reduces
this to the calculation of the homology groups of the order complex of
the lower interval (C^n,V) for V \neq C^n in the lattice of interesections

of the arrangements. This is the set of all linear subspaces that can be
formed by intersecting some set of subspaces of the arrangement ordered
by reversed inclusion. The order complex simply is the set of all chains
this interval. Actually I am cheating here since you will end up
with the cohomology of the complement, cohomology of the intervals
will give you homology of the complement.
For a fixed arrangement A you need to construct this poset in GAP. Now the

homology groups of the intervals can be computes by a to be proposed share
that Jean-Guileaume Dumas, Frank Heckenbach, Dave Saunders and
myself are currently designing. In case you are interested , let me know.

Best regards
Volkmar Welker


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