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pro vyhledávání: '"Aougab, Tarik"'
Autor:
Aougab, Tarik, Athreya, Jayadev
Let $\Sigma$ be a closed orientable hyperbolic surface. We introduce the notion of a \textit{geodesic current with corners} on $\Sigma$, which behaves like a geodesic current away from certain singularities (the "corners"). We topologize the space of
Externí odkaz:
http://arxiv.org/abs/2310.11556
A note on an effective characterization of covers with an application to higher rank representations
In this note we prove an effective characterization of when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of which curves have simple elevations, weakening the hypotheses to consi
Externí odkaz:
http://arxiv.org/abs/2307.09643
We prove that every closed orientable surface S of negative Euler characteristic admits a pair of finite-degree covers which are length isospectral over S but generically not simple length isospectral over S. To do this, we first characterize when tw
Externí odkaz:
http://arxiv.org/abs/2210.16706
Autor:
Aougab, Tarik, Gaster, Jonah
We study topological properties of random closed curves on an orientable surface $S$ of negative Euler characteristic. Letting $\gamma_{n}$ denote the conjugacy class of the $n^{th}$ step of a simple random walk on the Cayley graph driven by a measur
Externí odkaz:
http://arxiv.org/abs/2209.11309
Publikováno v:
Pacific J. Math. 317 (2022) 1-20
Let $S_{g}$ denote the closed orientable surface of genus $g$. In joint work with Huang, the first author constructed exponentially-many (in $g$) mapping class group orbits of pairs of simple closed curves whose complement is a single topological dis
Externí odkaz:
http://arxiv.org/abs/2108.10268
In this paper we consider two piecewise Riemannian metrics defined on the Culler-Vogtmann outer space which we call the entropy metric and the pressure metric. As a result of work of McMullen, these metrics can be seen as analogs of the Weil-Petersso
Externí odkaz:
http://arxiv.org/abs/2009.13314
Autor:
Aougab, Tarik, Gaster, Jonah
We show that any set of distinct homotopy classes of simple closed curves on the torus that pairwise intersect at most $k$ times has size $k + O(\sqrt{k} \log k)$. Prior to this work, a lemma of Agol, together with the state of the art bounds for the
Externí odkaz:
http://arxiv.org/abs/2008.08172
Publikováno v:
Math. Ann. 381 (2021), 459-498
Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper, we give a nearly complete classification of such groups for infinite-g
Externí odkaz:
http://arxiv.org/abs/2007.01982
Given two finite covers $p: X \to S$ and $q: Y \to S$ of a connected, oriented, closed surface $S$ of genus at least $2$, we attempt to characterize the equivalence of $p$ and $q$ in terms of which curves lift to simple curves. Using Teichm\"uller th
Externí odkaz:
http://arxiv.org/abs/2006.16988
Autor:
Agrawal, Shuchi, Aougab, Tarik, Chandran, Yassin, Loving, Marissa, Oakley, J. Robert, Shapiro, Roberta, Xiao, Yang
Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of such curves a
Externí odkaz:
http://arxiv.org/abs/1912.07666