Automorphisms of free groups with boundaries

Details Automorphisms of free groups with boundaries Automorphisms of free groups with boundaries

2004-02-11

arxiv.org/abs/math/0402166v2

Algebr. Geom. Topol. 4 (2004) 543-569

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-25.abs.html

Scientific paper

The automorphisms of free groups with boundaries form a family of groups A_{n,k} closely related to mapping class groups, with the standard automorphisms of free groups as A_{n,0} and (essentially) the symmetric automorphisms of free groups as A_{0,k}. We construct a contractible space L_{n,k} on which A_{n,k} acts with finite stabilizers and finite quotient space and deduce a range for the virtual cohomological dimension of A_{n,k}. We also give a presentation of the groups and calculate their first homology group.

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