The cohomological dimension of ann-manifold isn+ 1

Non-manifold Hyperbolic Groups of High Cohomological Dimension

Cohomological classification of Ann-categories

An Ann-category is a categorification of rings. Regular Ann-categories were classified by Shukla cohomology of algebras. In this paper, we state and prove the precise theorem on classification of Ann-categories in the general case based on Mac Lane cohomology of rings. AMS subject classifications: 18D10, 16E40

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 ...

Questions on Lie Algebras of Cohomological Dimension 1

A Lie algebra L is said to be of cohomological dimension 1, if H(L, M) = 0 for any L-module M . Due to the standard interpretation of the second cohomology group, this is equivalent to the condition that each exact sequence 0 → M → G → L → 0 splits. Of course, the cohomological dimension may be defined via standard devices of homological algebra – e.g. as the minimal length of the projective re...

On the left and right cohomological dimension

In this paper we construct, for any 1 m; n 1, a nitely presented monoid with left cohomological dimension m and right cohomological dimension n.