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

collaborators

Showing 2007Show all

4 papers · 1 filter

math.GT2007★ 36 cited

Intersection form, laminations and currents on free groups

Ilya Kapovich, Martin Lustig

Let $F_{N}$ be a free group of rank $N \geq 2$ , let $μ$ be a geodesic current on $F_{N}$ and let $T$ be an $R$ -tree with a very small isometric action of $F_{N}$ . We prove that the…

math.GR2007★ 47 cited

Geometric Intersection Number and analogues of the Curve Complex for free groups

Ilya Kapovich, Martin Lustig

For the free group $F_{N}$ of finite rank $N \geq 2$ we construct a canonical Bonahon-type continuous and $O u t (F_{N})$ -invariant \emph{geometric intersection form} \[ <, >: \bar{cv}(…

math.GR2007

Some Quantitative Aspects of Fractional Computability

Ilya Kapovich, Paul Schupp

Motivated by results on generic-case complexity in group theory, we apply the ideas of effective Baire category and effective measure theory to study complexity classes of function…

math.GR2007

On group-theoretic models of randomness and genericity

Ilya Kapovich, Paul Schupp

We compare the random group model of Gromov and the model of generic groups of Arzhantseva and Ol'shanskii.