Zobrazeno 1 - 10
of 94
pro vyhledávání: '"Dranishnikov, A N"'
Autor:
Chigogidze, A., Dranishnikov, A. N.
We give a short answer to the question in the title: {\em dendrits}. Precisely we show that the $C^{\ast}$-algebra $C(X)$ of all complex-valued continuous functions on a compactum $X$ is projective in the category ${\mathcal C}^{1}$ of all (not neces
Externí odkaz:
http://arxiv.org/abs/0902.3020
It follows from a theorem of Gromov that the stable systolic category of a closed manifold is bounded from below by the rational cup-length of the manifold. In the paper we study the inequality in the opposite direction. In particular, combining our
Externí odkaz:
http://arxiv.org/abs/0812.4637
Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length of a product of systoles that can form a curvature-free lower bound for the total volume of M, in the spirit of M. Gromov's systolic inequalities. Here n is the dimension o
Externí odkaz:
http://arxiv.org/abs/0807.5040
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher dimensions. We al
Externí odkaz:
http://arxiv.org/abs/0805.1527
We prove that for any group of the cohomological dimension $n$ the $n$th power of the Berstein class of the group is nontrivial. This allows to prove the following Berstein-Svarc theorem for all $n$: Theorem. For a connected complex $X$ with $\dim X=
Externí odkaz:
http://arxiv.org/abs/0712.2087
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher dimensions. We ex
Externí odkaz:
http://arxiv.org/abs/0706.1625
Autor:
Dranishnikov, A. N.
We introduce the notion of asymptotic cohomology based on the bounded cohomology and define cohomological asymptotic dimension $\as_{\Z} X$ of metric spaces. We show that it agrees with the asymptotic dimension $\as X$ when the later is finite. Then
Externí odkaz:
http://arxiv.org/abs/math/0608215
Autor:
Dranishnikov, A. N., Smith, J.
For a large class of metric space X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdim X of X coincides with the covering dimension $\dim(\nu_L X)$ of the Higson corona of X with respect to the sublinear coarse s
Externí odkaz:
http://arxiv.org/abs/math/0607143
Autor:
Dranishnikov, A. N.
Bestvina and Mess [BM] proved a remarkable formula for torsion free hyperbolic groups $$ \dim_L\partial\Gamma=cd_L\Gamma-1 $$ connecting the cohomological dimension of a group $\Gamma$ with the cohomological dimension of its boundary $\partial\Gamma$
Externí odkaz:
http://arxiv.org/abs/math/0503018
Autor:
Dranishnikov, A. N.
Publikováno v:
Topology Atlas Invited Contributions 6, no. 3 (2001) 61 pp
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
Comment: 61 pages
Comment: 61 pages
Externí odkaz:
http://arxiv.org/abs/math/0501523