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Morse Theory and Orbit Spaces of Subgroup Complexes-A New Proof of a Conjecture of Webb
by
Kai-Uwe Bux
Johann Wolfgang Goethe - University (Frankfurt, Germany)
Consider a finite group G and a prime number p. Form the directed graph whose vertices are the non-trivial p-subgroups of G and whose edges correspond to pairs Q < P of p-subgroups where Q is normal in P. Let X be the associated flag complex (fill in simplices if you can see their 1-sceleton). The group G acts on this complex by conjugation. Peter Webb conjectured and Peter Symbonds has proved that the orbit space X/G is contractible.
We will show that it is in fact a regular cell complex that even can be collapsed to a point. The proof uses a combination of a simple induction argument with Morse theory on cell complexes.
Date received: February 5, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-26.