A class of spaces with infinite cohomological dimension.

Cohomological Dimension Theory of Compact Metric Spaces

0. Introduction 1 1. General properties of the cohomological dimension 2 2. Bockstein theory 6 3. Cohomological dimension of Cartesian product 10 4. Dimension type algebra 15 5. Realization theorem 19 6. Test spaces 24 7. Infinite-dimensional compacta of finite cohomological dimension 28 8. Resolution theorems 33 9. Resolutions preserving cohomological dimensions 41 10. Imbedding and approximat...

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 ...

Cohomological Dimension of Markov Compacta

We rephrase Gromov’s definition of Markov compacta, introduce a subclass of Markov compacta defined by one building block and study cohomological dimensions of these compacta. We show that for a Markov compactum X, dimZ(p) X = dimQ X for all but finitely many primes p where Z(p) is the localization of Z at p. We construct Markov compacta of arbitrarily large dimension having dimQ X = 1 as well ...

A New Class of Banach Sequence Spaces

Cohomological Approach to Asymptotic Dimension

We introduce the notion of asymptotic cohomology based on the bounded cohomology and define cohomological asymptotic dimension asdimZ X of metric spaces. We show that it agrees with the asymptotic dimension asdimX when the later is finite. Then we use this fact to construct an example of a metric space X of bounded geometry with finite asymptotic dimension for which asdim(X × R) = asdimX. In pa...