Automorphisms of free groups with boundaries. (English) Zbl 1054.20023

Jensen, Craig A.; Wahl, Nathalie

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

The group \(A_{n,k}\) of automorphisms of a free group of rank \(n\) with \(k\) boundaries was introduced by the second author to show that the natural map from the stable mapping class group of surfaces to the stable automorphism group of free groups gives an infinite loop map on the classifying spaces of the groups after plus construction. There are geometrical and algebraical definitions of the groups considered.
In the paper under review a contractible space \(L_{n,k}\) is constructed on which \(A_{n,k}\) acts with finite stabilizers and finite quotient space. So a range of the virtual cohomological dimension of \(A_{n,k}\) is deduced.

Reviewer: V. A. Roman’kov (Omsk)

MSC:

20F65	Geometric group theory
20F28	Automorphism groups of groups
20E05	Free nonabelian groups

Keywords:

automorphism groups; mapping class groups; boundaries; free groups; virtual cohomological dimension; classifying spaces

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