Arc and curve graphs for infinite-type surfaces
Authors:
Javier Aramayona, Ariadna Fossas and Hugo Parlier
Journal:
Proc. Amer. Math. Soc. 145 (2017), 4995-5006
MSC (2010):
Primary 57M15, 57M50; Secondary 05C63
DOI:
https://doi.org/10.1090/proc/13608
Published electronically:
August 7, 2017
MathSciNet review:
3692012
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Abstract | References | Similar Articles | Additional Information
Abstract: We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite diameter; this extends a recent result of J. Bavard to a large class of punctured surfaces.
We also study the subgraph of the curve graph spanned by those elements which intersect a fixed separating curve on the surface. We show that this graph has infinite diameter and geometric rank 3, and thus is not hyperbolic.
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Additional Information
Javier Aramayona
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain
Email:
aramayona@gmail.com
Ariadna Fossas
Affiliation:
Department of Mathematics, University of Fribourg, Chemin du Musée 23, CH-1700 Fribourg, Switzerland
Email:
ariadna.fossastenas@gmail.com
Hugo Parlier
Affiliation:
Department of Mathematics, University of Fribourg, Chemun du Musée 23, CH-1700, Fribourg, Switzerland
Address at time of publication:
Mathematics Research Unit, University of Luxembourg, 4364, Esch-sur-Alzette, Luxembourg
Email:
hugo.parlier@uni.lu
DOI:
https://doi.org/10.1090/proc/13608
Received by editor(s):
April 29, 2016
Received by editor(s) in revised form:
August 23, 2016, and November 4, 2016
Published electronically:
August 7, 2017
Additional Notes:
The first author was supported by a Ramón y Cajal grant RYC-2013-13008
The second author was supported by ERC grant agreement number 267635 - RIGIDITY
The third author was supported by Swiss National Science Foundation grants numbers PP00P2_128557 and PP00P2_153024
The authors acknowledge support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 “NMS: Geometric structures and representation varieties” (the GEAR Network)
Communicated by:
Ken Bromberg
Article copyright:
© Copyright 2017
American Mathematical Society
