Zobrazeno 1 - 10
of 500
pro vyhledávání: '"Sapir M"'
Autor:
Olshanskii, A. Yu., Sapir, M. V.
We construct and study finitely presented groups with quadratic Dehn function (QD-groups) and present the following applications of the method developed in our recent papers. (1) The isomorphism problem is undecidable in the class of QD-groups. (2) F
Externí odkaz:
http://arxiv.org/abs/2012.10417
Autor:
Olshanskii, A. Yu., Sapir, M. V.
We prove that for every $r>0$ if a non-positively curved $(p,q)$-map $M$ contains no flat submaps of radius $r$, then the area of $M$ does not exceed $Crn$ for some constant $C$. This strengthens a theorem of Ivanov and Schupp. We show that an infini
Externí odkaz:
http://arxiv.org/abs/1702.08205
We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function. The group
Externí odkaz:
http://arxiv.org/abs/1204.6506
Autor:
Olshanskii, A. Yu., Sapir, M. V.
A $k$-free like group is a $k$-generated group $G$ with a sequence of $k$-element generating sets $Z_n$ such that the girth of $G$ relative to $Z_n$ is unbounded and the Cheeger constant of $G$ relative to $Z_n$ is bounded away from 0. By a recent re
Externí odkaz:
http://arxiv.org/abs/0811.1607
The main goal of this paper is a detailed study of asymptotic cones of the mapping class groups. In particular, we prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real trees, sendin
Externí odkaz:
http://arxiv.org/abs/0810.5376
Autor:
Sapir, M. V.
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some necessary defi
Externí odkaz:
http://arxiv.org/abs/0704.2899
Autor:
Ol'shanskii, A. Yu., Sapir, M. V.
We construct a 2-generated 2-related group without non-trivial finite factors. That answers a question of J. Button.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/0704.2897
We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity constants
Externí odkaz:
http://arxiv.org/abs/math/0701365
Autor:
Olshanskii, A. Yu., Sapir, M. V.
We give an example of a finitely presented group $G$ with two non-$\pi_1$-equivalent asymptotic cones.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/math/0504350
Autor:
Olshanskii, A. Yu., Sapir, M. V.
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/math/0405337