Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Pfaff, Catherine"'
We show that the group $\langle a,b,c,t : a^t=b,b^t=c,c^t=ca^{-1} \rangle$ is profinitely rigid amongst free-by-cyclic groups, providing the first example of a hyperbolic free-by-cyclic group with this property.
Comment: 4 pages. Comments welcom
Comment: 4 pages. Comments welcom
Externí odkaz:
http://arxiv.org/abs/2410.17817
Autor:
Pfaff, Catherine Eva
We describe train track automata for large classes of fully irreducible elements of Out($F_r$), and their associated geodesics in Culler-Vogtmann Outer Space.
Externí odkaz:
http://arxiv.org/abs/2409.05599
We find the shortest realized stretch factor for a fully irreducible $\varphi\in\mathrm{Out}(F_3)$ and show that it is realized by a "principal" fully irreducible element. We also show that it is the only principal fully irreducible produced by a sin
Externí odkaz:
http://arxiv.org/abs/2405.03681
Autor:
Cooper, Daryl, Pfaff, Catherine
We defined a new set of coordinates with respect to which the Thurston compactification of Teichmuller space is the radial compactification of Euclidean space.
Externí odkaz:
http://arxiv.org/abs/2404.17081
Autor:
Pfaff, Catherine, Hunter, Emily, Hong, Haozhi, Forestell, Daniel, Fialkov, Ari, Drassinower, Zoey, Chan, Timothy
In this paper, we examine how soccer players can use their spatial relationships to control parts of the field and safely move play up the field via chains of ``safe configurations,'' i.e. configurations of players on a team ensuring the possessor of
Externí odkaz:
http://arxiv.org/abs/2210.16474
Autor:
Gagnier, Damara, Pfaff, Catherine
Principal outer automorphisms were introduced in Algom-Kfir-Kapovich-Pfaff to emulate principal pseudo-Anosov surface homeomorphisms, i.e. those whose attracting and repelling invariant foliations have only 3-pronged singularities. It is proved in Al
Externí odkaz:
http://arxiv.org/abs/2011.14913
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
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
In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichm\"uller space $\mathcal{T}(S)$ of a closed hyperbolic surface $S$. More specifically, we focus on properties of the geodesics in Teichm
Externí odkaz:
http://arxiv.org/abs/1706.00673