Minimal 4-manifolds for groups of cohomological dimension 2

Virtual Cohomological Dimension of Mapping Class Groups of 3-manifolds

The mapping class group of a topological space is the group of self-homeomorphisms modulo the equivalence relation of isotopy. For 2-manifolds (of finite type), it is a discrete group which is known (see [M, HI, H2, H3, H4]) to share many of the properties of arithmetic subgroups of linear algebraic groups, although it is not arithmetic. In this note we describe the results of [Ml], which show ...

Automorphisms of Pro-p groups of finite virtual cohomological dimension

Let G be a pro-p group of finite cohomological dimension and type FP∞ and T is a finite p-group of automorphisms of G. We prove that the group of fixed points of T in G is again a pro-p group of type FP∞ (in particular it is finitely presented). Moreover we prove that a pro-p group G of type FP∞ and finite virtual cohomological dimension has finitely many conjugacy classes of finite subgroups.

Normal subgroups of profinite groups of finite cohomological dimension

We study a profinite group G of finite cohomological dimension with (topologically) finitely generated closed normal subgroup N . If G is pro-p and N is either free as a pro-p group or a Poincaré group of dimension 2 or analytic pro-p, we show that G/N has virtually finite cohomological dimension cd(G) − cd(N). Some other cases when G/N has virtually finite cohomological dimension are considere...

Non-manifold Hyperbolic Groups of High Cohomological Dimension

M ay 2 00 4 DIMENSION GROUPS FOR INTERVAL MAPS

With each piecewise monotonic map τ of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t −1 ] module , is finitely generated, and generators are identified. Dimension groups are computed for Markov maps, unimodal maps, multimodal maps, and interval exchange maps. It is shown that the dimension group defined here is isomor-phic to K 0 (A), where A is a...