Geodesic
Hyperbolicity of the graph of nonseparating multicurves
Hamenstädt, Ursula1
1Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1759-1778
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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 < g∕2 + 1, then NC(S,k) is hyperbolic.

DOI : 10.2140/agt.2014.14.1759
Classification : 57M50, 20F65, 57M99
Keywords: multicurve graph, hyperbolicity

Hamenstädt, Ursula  1

1 Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany 
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Hamenstädt, Ursula. Hyperbolicity of the graph of nonseparating multicurves. Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1759-1778. doi: 10.2140/agt.2014.14.1759

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