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2020 Finite rigid sets in arc complexes
Emily Shinkle
Algebr. Geom. Topol. 20(6): 3127-3145 (2020). DOI: 10.2140/agt.2020.20.3127

Abstract

For any compact, connected, orientable, finite-type surface with marked points other than the sphere with three marked points, we construct a finite rigid set of its arc complex: a finite simplicial subcomplex of its arc complex such that any locally injective map of this set into the arc complex of another surface with arc complex of the same or lower dimension is induced by a homeomorphism of the surfaces, unique up to isotopy in most cases. It follows that if the arc complexes of two surfaces are isomorphic, the surfaces are homeomorphic. We also give an exhaustion of the arc complex by finite rigid sets. This extends the results of Irmak and McCarthy (Turkish J. Math. 34 (2010) 339–354).

Citation

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Emily Shinkle. "Finite rigid sets in arc complexes." Algebr. Geom. Topol. 20 (6) 3127 - 3145, 2020. https://doi.org/10.2140/agt.2020.20.3127

Information

Received: 7 October 2019; Revised: 20 January 2020; Accepted: 17 February 2020; Published: 2020
First available in Project Euclid: 16 December 2020

MathSciNet: MR4185937
Digital Object Identifier: 10.2140/agt.2020.20.3127

Subjects:
Primary: 20F38 , 20F65 , 57M60 , 57N05

Keywords: arc , arc complex , finite rigid , geometric topology , rigidity , simplicial complex

Rights: Copyright © 2020 Mathematical Sciences Publishers

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