Sphere systems, intersections and the geometry of $\mathrm{Out}(F_n)$

Details Sphere systems, intersections and the geometry of $\mathrm{Out}(F_n)$ Sphere systems, intersections and the geometry of $\mathrm{Out}(F_n)$

2011-09-13

arxiv.org/abs/1109.2687v1

Mathematics

Geometric Topology

26 pages, 2 figures

Scientific paper

The outer automorphism group $\mathrm{Out}(F_{2g})$ of a free group on $2g$ generators naturally contains the mapping class group of a punctured surface as a subgroup. Using topological methods in a suitable 3-manifold we show that this subgroup is undistorted. We also use topological techniques to give a new proof of a result of Handel and Mosher stating that stabilizers of conjugacy classes of free splittings and corank 1 free factors in a free group $F_n$ are undistorted in $\mathrm{Out}(F_n)$.

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