Spheres and Projections for $\mathrm{Out}(F_n)$
Geometric Topology
2017-05-17 v3 Group Theory
Abstract
The outer automorphism group Out(F_2g) of a free group on 2g generators naturally contains the mapping class group of a punctured surface as a subgroup. We define a subsurface projection of the sphere complex of the connected sum of n copies of S^1 x S^2 into the arc complex of the surface and use this to show that this subgroup is a Lipschitz retract of Out(F_2g). We also use subsurface projections to give a simple proof of a result of Handel and Mosher [HM10] stating that stabilizers of conjugacy classes of free splittings and corank 1 free factors in a free group Fn are Lipschitz retracts of Out(F_n).
Cite
@article{arxiv.1109.2687,
title = {Spheres and Projections for $\mathrm{Out}(F_n)$},
author = {Ursula Hamenstädt and Sebastian Hensel},
journal= {arXiv preprint arXiv:1109.2687},
year = {2017}
}
Comments
32 pages, 9 figures