Ilya Kapovich

activity

19952026

most citedGeometric Intersection Number and analogues of the Curve Complex for free groups

47 citations · 349 across the 75 of their papers we have counts for

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7 papers · 1 filter

math.GR2026

Uniquely Ergodic Branching Subset Currents on Free and Surface Groups

Ilya Kapovich

\emph{Subset currents} on free groups, on surface groups and, more generally, on word-hyperbolic groups, were introduced by Kapovich and Nagnibeda, and further studied by Sasaki. S…

math.GR2026

Small Cancellation Stability and Isomorphism Rigidity for Generic Finitely Presented Groups

Ilya Kapovich

Let $F_{m} = F (a_{1}, \dots, a_{m})$ with $m \geq 2$ , and fix $q \geq 1$ . For every fixed $0 < λ < 1$ , we prove that a $q$ -tuple $W_{n}$ of independent uniformly random cyclically reduced word…

math.GR2026

Nielsen classes in outer automorphism groups of free groups

Ilya Kapovich

For every $n \geq 8$ , we construct explicit families of generating pairs of $G L (n, Z)$ and $S L (n, Z)$ representing countably infinitely many Nielsen equivalence classes…

math.GR2026

Sequence distortion for metric spaces

Ilya Kapovich

We introduce \emph{sequence distortion spectrum}, a quasi-isometry invariant recording the large-scale distance profiles of sequences indexed by $N$ or $Z$ in a met…

math.GR2026

Compressed primitivity problem in free groups

Ilya Kapovich

For a fixed integer $r \geq 2$ , we prove that the \emph{compressed primitivity problem} in the free group $F_{r} = F (x_{1}, \dots, x_{r})$ is decidable in non-deterministic polynomial time. Th…

math.GR2026

On Dehn functions for infinite group presentations

Ilya Kapovich

We study the behavior of Dehn functions of finitely presentable groups for presentations with finite generating sets and possibly infinite sets of defining relators. For the free a…