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.
Algebraic & Geometric Topology
Jensen, Craig A.; Wahl, Nathalie Automorphisms of free groups with boundaries. Algebr. Geom. Topol. 4 (2004), 543–569.