We prove that the cohomological dimension of the Torelli group for a closed connected orientable surface of genus g â‰¥ 2 is equal to 3g âˆ’ 5. This answers a question of Mess, who proved the lower boundâ€¦ (More)

We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FPâˆž by comparing its large-scale geometry to the large-scale geometry of lattices in realâ€¦ (More)

Let Tn be the kernel of the natural map Out(Fn) â†’ GLn(Z). We use combinatorial Morse theory to prove that Tn has an Eilenbergâ€“MacLane space which is (2n âˆ’ 4)-dimensional and that H2nâˆ’4(Tn, Z) is notâ€¦ (More)

While there are numerous results on the congruence subgroup problem for arithmetic groups (cf. [10] for a recent survey), very little is known regarding (*) for the automorphism groups of generalâ€¦ (More)

Let G be a Chevalley group scheme and B â‰¤ G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K , and OS be the correspondingâ€¦ (More)

We compute the virtual cohomological dimension (VCD) of the group of partially symmetric outer automorphisms of a free group. We use this to obtain new upper and lower bounds on the VCD of the outerâ€¦ (More)

It is known from work by H. Abels and P. Abramenko that for a classical Fqgroup G of rank n the arithmetic lattice G(Fq[t]) of Fq[t]-points is of type Fnâˆ’1 provided that q is large enough. We showâ€¦ (More)

Let G be a Chevalley group scheme and B G a Borel subgroup scheme, both de ned over Z. Let K be a global function eld, S be a nite non-empty set of places over K , and OS be the correspondingâ€¦ (More)

Outer automorphism groups of free groups provide interesting analogues of mapping class groups and arithmetic groups. Iâ€™ll discuss homological decompositions of Out(Fn) that take their roots in theâ€¦ (More)