Bonn Topology Group - Abstracts
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Talk
QAYUM KHAN (Notre Dame): Involutions on tori with isolated fixed points (24 May 2011)
Abstract
We prove there is only one involution (up to conjugacy) on the
n-torus which acts as -Id on the first homology group when n is of
the form 4k, is of the form 4k+1, or is less than 4. In all other
cases we prove there are infinitely many such involutions up to
conjugacy, but each of them has exactly 2^n fixed points and is
conjugate to a smooth involution. The key technical point is that
we completely compute the equivariant structure set for the
corresponding crystallographic group action on R^n in terms of the
Cappell UNil-groups arising from its infinite dihedral subgroups.
We give a complete analysis of equivariant topological rigidity for
this family of groups.
This is joint work with Frank Connolly and Jim Davis. It is
available online at http://arxiv.org/abs/1102.2660
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