# COHOMOLOGICAL DIMENSION THEORY OF COMPACT METRIC SPACES

@article{Dranishnikov2001COHOMOLOGICALDT, title={COHOMOLOGICAL DIMENSION THEORY OF COMPACT METRIC SPACES}, author={Alexander Dranishnikov}, journal={arXiv: General Topology}, year={2001} }

This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.

## 73 Citations

General Position Properties in Fiberwise Geometric Topology

- Mathematics
- 2010

The book is devoted to constructing embedding finite-dimensional maps into trivial bundles and investigating the corresponding general position properties.

Dimension of maps, universal spaces, and homotopy

- Mathematics
- 2008

This paper is a survey of some recent results in dimension theory. The main topics under consideration are: dimension of maps in the classical and extension dimension theories, universal spaces (in…

Extensions of maps to Moore spaces

- Mathematics
- 2015

We show that a Moore space M(ℤm, 1) is an absolute extensor for finite-dimensional metrizable spaces of cohomological dimension at most one with respect to the group ℤm. Applications of this result…

Asymptotic Dimension

- Mathematics
- 2007

The asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension…

Extensions of maps to M(Z_m,1)

- Mathematics
- 2013

We show that a Moore space M(Z_m,1) is an absolute extensor for finite dimensional metrizable spaces of cohomological dimension dim_{Z_m} \leq 1.

A dimensional property of Cartesian product

- Mathematics
- 2012

We show that the Cartesian product of three hereditarily infinite dimensional compact metric spaces is never hereditarily infinite dimensional. It is quite surprising that the proof of this fact (and…

## References

SHOWING 1-10 OF 67 REFERENCES

Spaces without cohomological dimension preserving compactifications

- Mathematics
- 1991

Examples are constructed that include: first, a separable metric space having cohomological dimension 4 such that every Hausdorff compactification has cohomological dimension at least 5; second, a…

Homological dimension theory

- Mathematics
- 1988

CONTENTS Introduction § 1. Definition of cohomological dimension § 2. Bokshtein's inequalities § 3. Cohomological manifolds over finite groups § 4. The CE-problem § 5. Borsuk's problem References

On the virtual cohomological dimensions of Coxeter groups

- Mathematics
- 1997

We apply Bestvina’s approach of calculation of the virtual cohomological dimension of Coxeter groups. The explicit formula for vcdFΓ in terms of cohomological properties of the corresponding complex…

Completion theorem for cohomological dimensions

- Mathematics
- 1995

We prove that for every separable metrizable space X with dimG X < n, there exists a metrizable completion Y of X with dimG Y < n provided that G is either a countable group or a torsion group, and…

K-THEORY ON THE CATEGORY OF INFINITE CELL COMPLEXES

- Mathematics
- 1968

The main purpose of the article is to compute cohomology operations in K-theory mod p and operations from the usual cohomology theory into K-theory. The proposed method is based on the extension of…

On the failure of the Urysohn-Menger sum formula for cohomological dimension

- Mathematics
- 1994

We prove that the classical Urysohn-Menger sum formula, dim(A U B) dimQ/z A + dimQ/z B + 1 = 3.

Rational homology manifolds and rational resolutions

- Mathematics
- 1999

Abstract We prove that every compactum X , having rational dimension n , is an image under a rationally acyclic map of an (n+1) -dimensional compactum Y . If n>1 , then additionally dim Q Y=n . As a…