Hyperbolicity of the graph of nonseparating multicurves

Hamenstädt, Ursula

doi:10.2140/agt.2014.14.1759

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Hyperbolicity of the graph of nonseparating multicurves

Ursula Hamenstädt

Algebraic & Geometric Topology 14 (2014) 1759–1778

DOI: 10.2140/agt.2014.14.1759

Abstract

A nonseparating multicurve on a surface $S$ of genus $g \geq 2$ with $m \geq 0$ punctures is a multicurve $c$ so that $S - c$ is connected. For $k \geq 1$ define the graph $N C (S, k)$ 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 $k < g ∕ 2 + 1$ , then $N C (S, k)$ 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

Volume 14, issue 3 (2014)