Geometry for palindromic automorphism groups of free groups

Details Geometry for palindromic automorphism groups of free groups Geometry for palindromic automorphism groups of free groups

2001-12-18

arxiv.org/abs/math/0112190v1

Comment. Math. Helv. 75 (2000) 644-667

Mathematics

Group Theory

Scientific paper

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

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