4 citations · 8 across the 12 of their papers we have counts for
11 papers · 1 filter
Genericity, the Arzhantseva-Ol'shanskii method and the Isomorphism Problem for One-Relator Groups
Ilya Kapovich, Paul Schupp
We apply the method of Arzhantseva-Ol'shanskii to prove that for an exponentially generic (in the sense of Ol'shanskii) class of one-relator groups the isomorphism problem is solva…
Acylindrical accessibility for groups acting on -trees
Ilya Kapovich, Richard Weidmann
We prove an acylindrical accessibility theorem for finitely generated groups acting on -trees. Namely, we show that if is a freely indecomposable non-cyclic -gene…
A remark on mapping tori of free group endomorphisms
Ilya Kapovich
We observe that the results of Feighn-Handel and Geoghegan-Mihalik-Sapir-Wise about coherence and Hopficity of mapping tori of injective endomorphisms of free groups extend to non-…
Average-case complexity and decision problems in group theory
Ilya Kapovich, Alexei Myasnikov, Paul Schupp +1
We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic…
The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups
Ilya Kapovich
We show that if is a quasiconvex subgroup of infinite index in a non-elementary hyperbolic group then the Schreier coset graph for relative to is non-amenable (…
Nielsen methods and groups acting on hyperbolic spaces
Ilya Kapovich, Richard Weidmann
We show that for any positive integer there exists a constant such that any -generated group , which acts by isometries on a -hyperbolic space (with ), i…