3 citations · 4 across the 7 of their papers we have counts for
9 papers · 1 filter
Densities in free groups and , Visible Points and Test Elements
Ilya Kapovich, Igor Rivin, Paul Schupp +1
In this article we relate two different densities. Let be the free group of finite rank and let be the abelianization map from onto . We pr…
The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms
Vadim Kaimanovich, Ilya Kapovich, Paul Schupp
Given a free group of rank with a fixed set of free generators we associate to any homomorphism from to a group with a left-invariant semi-norm a gener…
Translation equivalence in free groups
Ilya Kapovich, Gilbert Levitt, Paul Schupp +1
Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study…
Delzant's T-invariant, Kolmogorov complexity and one-relator groups
Ilya Kapovich, Paul Schupp
We prove that ``almost generically'' for a one-relator group Delzant's -invariant (which measures the smallest size of a finite presentation for a group) is comparable in magnit…
Generic properties of Whitehead's Algorithm and isomorphism rigidity of random one-relator groups
Ilya Kapovich, Paul Schupp, Vladimir Shpilrain
We prove that Whitehead's algorithm for solving the automorphism problem in a fixed free group has strongly linear time generic-case complexity. This is done by showing that…
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…