Automorphisms of free groups with boundaries

Craig A. Jensen; Nathalie Wahl

doi:10.2140/agt.2004.4.543

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Automorphisms of free groups with boundaries

Craig A. Jensen·Nathalie Wahl

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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.

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BibTeX RIS

Craig A. Jensen, Nathalie Wahl. 2004-07-24. Automorphisms of free groups with boundaries. https://doi.org/10.2140/agt.2004.4.543

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