32 citations · 54 across the 5 of their papers we have counts for
5 papers
Algorithmically complex residually finite groups
O. Kharlampovich, A. Myasnikov, M. Sapir
We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arb…
Median structures on asymptotic cones and homomorphisms into mapping class groups
J. Behrstock, C. Drutu, M. Sapir
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 b…
Lacunary hyperbolic groups
A. Yu. Olshanskii, D. V. Osin, M. V. Sapir
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…
Diagram groups and directed 2-complexes: homotopy and homology
V. S. Guba, M. V. Sapir
We show that diagram groups can be viewed as fundamental groups of spaces of positive paths on directed 2-complexes (these spaces of paths turn out to be classifying spaces). Thus…
Isoperimetric Functions of Groups and Computational Complexity of the Word Problem
J. -C. Birget, A. Yu. Olshanskii, E. Rips +1
We prove that the word problem of a finitely generated group is in NP (solvable in polynomial time by a non-deterministic Turing machine) if and only if this group is a subgrou…