Edge-preserving maps of curve graphs

2016/11/25 by Jesús Hernández Hernández, Hernández, Jesús Hernández
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1611.08328

23 pages, 22 figures

arxiv created 2016/11/25 · arxiv updated 2016/11/28

Abstract

Suppose S₁ and S₂ are orientable surfaces of finite topological type such that S₁ has genus at least 3 and the complexity of S₁ is an upper bound of the complexity of S₂. Let φ: C(S₁) → C(S₂) be an edge-preserving map; then S₁ is homeomorphic to S₂, and in fact φ is induced by a homeomorphism. To prove this, we use several simplicial properties of rigid expansions, which we prove here.

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