English

Geometry for palindromic automorphism groups of free groups

Group Theory 2007-05-23 v1 Algebraic Topology

Abstract

We examine the palindromic automorphism group ΠA(Fn)\Pi A(F_n) of a free group FnF_n, a group first defined by Collins which is related to hyperelliptic involutions of mapping class groups, congruence subgroups of SLn(Z)SL_n(\Z), and symmetric automorphism groups of free groups. Cohomological properties of the group are explored by looking at a contractible space on which ΠA(Fn)\Pi A(F_n) acts properly with finite quotient. Our results answer some conjectures of Collins and provide a few striking results about the cohomology of ΠA(Fn)\Pi A(F_n), such as that its rational cohomology is zero at the vcd.

Keywords

Cite

@article{arxiv.math/0112190,
  title  = {Geometry for palindromic automorphism groups of free groups},
  author = {Henry H Glover and Craig A. Jensen},
  journal= {arXiv preprint arXiv:math/0112190},
  year   = {2007}
}
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