We prove that the reduced C -algebras of centerless mapping class groups and outer automorphism groups of free groups are simple, as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer automorphism groups of free groups. r 2003 Elsevier Inc. All rights reserved. MSC: 20F28; 20F65; 46L55; 57N05

Let W be a right-angled Coxeter group. We characterize the centralizer of the Coxeter element of a finite special subgroup of W. As an application, we give a solution to the generalized word problem for Inn(W ) in Aut(W ). Mathematics Subject Classification: 20F10, 20F28, 20F55

We determine the number ω(G) of orbits on the (finite) group G under the action of Aut(G) for G ∈ {PSL(2, q),SL(2, q),PSL(3, 3),Sz(2)}, covering all of the minimal simple groups as well as all of the simple Zassenhaus groups. This leads to recursive formulae on the one hand, and to the equation ω(Sz(q)) = ω(PSL(2, q)) + 2 on the other. MSC 20E32, 20F28, 20G40, 20-04

We examine the palindromic automorphism group ΠA(Fn) of a free group Fn, a group first defined by Collins in [5] which is related to hyperelliptic involutions of mapping class groups, congruence subgroups of SLn(Z), and symmetric automorphism groups of free groups. Cohomological properties of the group are explored by looking at a contractible space on which ΠA(Fn) acts properly with finite quo...

A graph G is singular of nullity (> 0), if its adjacency matrix A is singular, with the eigenvalue zero of multiplicity . A singular graph having a 0-eigenvector, x, with no zero entries, is called a core graph.We place particular emphasis on nut graphs, namely the core graphs of nullity one. Through symmetry considerations of the automorphism group of the graph, we study relations among the en...

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 cohomolog...

We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F2) of automorphisms of the rank two free group F2 and show that it can be realized as a monoid in the group B4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F2 lifting any given basis of the free abelian group Z . ...

We show that for every finite subgroup G of Aut(Fn), the fixed point subcomplex X n is contractible, where Fn is the free group on n letters and Xn is the spine of “auter space” constructed by Hatcher and Vogtmann in [6]. In more categorical language, Xn = EAut(Fn). This is useful because it allows one to compute (see, for example, [7, 8]) the cohomology of normalizers or centralizers of finite...

Let Fn be the free group on n generators. Define IAn to be group of automorphisms of Fn that act trivially on first homology. The Johnson homomorphism in this setting is a map from IAn to its abelianization. The first goal of this paper is to determine how much this map contributes to the second rational cohomology of IAn . A descending central series of IAn is given by the subgroups K (i) n wh...