Automorphisms of free groups with boundaries

Jensen, Craig¹ ; Wahl, Nathalie²

¹Department of Mathematics, University of New Orleans, New Orleans LA 70148, USA
²Department of Mathematics, University of Aarhus, Ny Munkegade 116, 8000 Aarhus, Denmark

Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 543-569

Résumé

The automorphisms of free groups with boundaries form a family of groups An,k closely related to mapping class groups, with the standard automorphisms of free groups as An,0 and (essentially) the symmetric automorphisms of free groups as A0,k. We construct a contractible space Ln,k on which An,k acts with finite stabilizers and finite quotient space and deduce a range for the virtual cohomological dimension of An,k. We also give a presentation of the groups and calculate their first homology group.

Détail

DOI : 10.2140/agt.2004.4.543

Keywords: automorphism groups, classifying spaces.

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