Zobrazeno 1 - 10
of 258
pro vyhledávání: '"Kapovich, Ilya"'
Autor:
Kapovich, Ilya
Motivated by a classic theorem of Birman and Series about the set of complete simple geodesics on a hyperbolic surface, we study the Hausdorff dimension of the set of endpoints in $\partial F_r$ of some abstract algebraic laminations associated with
Externí odkaz:
http://arxiv.org/abs/2410.02058
We prove that if $G_\phi=\langle F, t| t x t^{-1} =\phi(x), x\in F\rangle$ is the mapping torus group of an injective endomorphism $\phi: F\to F$ of a free group $F$ (of possibly infinite rank), then every two-generator subgroup $H$ of $G_\phi$ is ei
Externí odkaz:
http://arxiv.org/abs/2405.08985
Autor:
Kapovich, Ilya
We prove that for any fixed integers $m\ge 2, t\ge 1, k\ge 2$ a generic $m$-generator $t$-relator group satisfies the Ascending Chain Condition for $k$-generated subgroups.
Comment: 12 pages, 1 figure
Comment: 12 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2306.06706
Autor:
Kapovich, Ilya
For a free group $F_r$ of finite rank $r\ge 2$ and a nontrivial element $w\in F_r$ the \emph{primitivity rank} $\pi(w)$ is the smallest rank of a subgroup $H\le F_r$ such that $w\in H$ and that $w$ is not primitive in $H$ (if no such $H$ exists, one
Externí odkaz:
http://arxiv.org/abs/2109.09400
Autor:
Kapovich, Ilya, Simon, Zachary
Motivated by results about "untangling" closed curves on hyperbolic surfaces, Gupta and Kapovich introduced the primitivity and simplicity index functions for finitely generated free groups, $d_{prim}(g;F_N)$ and $d_{simp}(g;F_N)$, where $1\ne g\in F
Externí odkaz:
http://arxiv.org/abs/2012.13655
Publikováno v:
Geom. Topol. 26 (2022) 127-162
We prove that for the harmonic measure associated to a random walk on Out$(F_r)$ satisfying some mild conditions, a typical tree in the boundary of Outer space is trivalent and nongeometric. This answers a question of M. Bestvina.
Comment: 28 pa
Comment: 28 pa
Externí odkaz:
http://arxiv.org/abs/1904.10026
Autor:
Kapovich, Ilya
In \cite{KSS06} it was shown that with respect to the simple non-backtracking random walk on the free group $F_N=F(a_1,\dots,a_N)$ the Whitehead algorithm has strongly linear time generic-case complexity and that "generic" elements of $F_N$ are "stri
Externí odkaz:
http://arxiv.org/abs/1903.07040
We prove that a "random" free group outer automorphism is an ageometric fully irreducible outer automorphism whose ideal Whitehead graph is a union of triangles. In particular, we show that its attracting (and repelling) tree is a nongeometric $\math
Externí odkaz:
http://arxiv.org/abs/1805.12382
Autor:
Kapovich, Ilya, Pfaff, Catherine
Publikováno v:
Geom. Dedicata 218 (2024), no. 2, Paper no. 39
Inspired by results of Eskin and Mirzakhani counting closed geodesics of length $\le L$ in the moduli space of a fixed closed surface, we consider a similar question in the $Out(F_r)$ setting. The Eskin-Mirzakhani result can be equivalently stated in
Externí odkaz:
http://arxiv.org/abs/1801.07471
Autor:
Hull, Michael, Kapovich, Ilya
We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentia
Externí odkaz:
http://arxiv.org/abs/1707.07095