Kai-Uwe Bux

Higher Finiteness Properties of Reductive Arithmetic Groups in Positive Characteristic: the Rank Theorem

We show that the niteness length of an S-arithmetic subgroup in a noncommutative isotropic absolutely almost simple groupG over a global function eld is one less than the sum of the local ranks of G taken over the places in S. This determines the niteness properties for S-arithmetic subgroups in isotropic reductive groups, conrming the conjectured niteness properties for this class of groups. Our main tool is Behr{Harder reduction theory which we recast in terms of the metric structure of euclidean buildings.

Dimension of the Torelli group for Out(Fn)

Let

The braided Thompson's groups are of type F∞

\mathcal{T}_{n}

Automorphisms of two-dimensional RAAGS and partially symmetric automorphisms of free groups

be the kernel of the natural map Out(Fn)→GLn(ℤ). We use combinatorial Morse theory to prove that

Finiteness properties of soluble arithmetic groups over global function fields

\mathcal{T}_{n}

A geometric proof that SL2(ℤ[t,t−1]) is not finitely presented

has an Eilenberg–MacLane space which is (2n-4)-dimensional and that

The congruence subgroup property for Aut

H_{2n-4}(\mathcal{T}_{n},\mathbb{Z})

F_2

is not finitely generated (n≥3). In particular, this shows that the cohomological dimension of

: A group-theoretic proof of Asada’s theorem

\mathcal{T}_{n}

SLn(ℤ[t]) is not FPn − 1

is equal to 2n-4 and recovers the result of Krstić–McCool that