Finiteness properties for a subgroup of the pure symmetric automorphism group
Group Theory
2009-09-20 v2 Geometric Topology
Abstract
Let F_n be the free group on n generators, and P\Sigma_n be the group of automorphisms of F_n which send each generator to a conjugate of itself. Let K_n be the kernel of the homomorphism from P\Sigma_n to P\Sigma_{n-1} induced by mapping one of the free group generators to the identity. We show that K_n has cohomological dimension n-1, and that the ith cohomology groups are infinitely generated for all i between 2 and n-1. It follows that K_n is not finitely presentable for n>2.
Keywords
Cite
@article{arxiv.math/0602148,
title = {Finiteness properties for a subgroup of the pure symmetric automorphism group},
author = {Alexandra Pettet},
journal= {arXiv preprint arXiv:math/0602148},
year = {2009}
}
Comments
Originally titled "Finiteness properties for the kernel of pure motions of n unlinked loops"; error in Lemma 3.2 removed; argument of main theorem simplified