Automorphisms of free groups with boundaries

Abstract

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.

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

References in corpus (1)

• Stabilization for the automorphisms of free groups with boundaries

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• Rational homological stability for groups of partially symmetric automorphisms of free groups
• Topological Field Theories and Harrison Homology
• Cutting and Pasting in the Torelli subgroup of Out($F_n$)