Volume 14, issue 3 (2014)

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Hyperbolicity of the graph of nonseparating multicurves

Ursula Hamenstädt

Algebraic & Geometric Topology 14 (2014) 1759–1778
Abstract

A nonseparating multicurve on a surface S of genus g 2 with m 0 punctures is a multicurve c so that S c is connected. For k 1 define the graph NC(S,k) of nonseparating k–multicurves to be the graph whose vertices are nonseparating multicurves with k components and where two such multicurves are connected by an edge of length one if they can be realized disjointly and differ by a single component. We show that if k < g2 + 1, then NC(S,k) is hyperbolic.

Keywords
multicurve graph, hyperbolicity
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 20F65, 57M99
References
Publication
Received: 20 April 2013
Revised: 29 September 2013
Accepted: 13 October 2013
Published: 29 May 2014
Authors
Ursula Hamenstädt
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
D-53115 Bonn
Germany