FINITE RIGID SETS IN CURVE COMPLEXES-Reference-Cited by-同舟云学术

FINITE RIGID SETS IN CURVE COMPLEXES

Published:2013-05-20 Issue:02 Volume:05 Page:183-203
ISSN:1793-5253
Container-title:Journal of Topology and Analysis
language:en
Short-container-title:J. Topol. Anal.

Author:

ARAMAYONA JAVIER¹,LEININGER CHRISTOPHER J.²

Affiliation:

1. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland at Galway, University Road, Galway, Ireland

2. University of Illinois at Urbana-Champaign, Urbana, IL, USA

Abstract

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex 𝔛 of the curve complex [Formula: see text] such that every locally injective simplicial map [Formula: see text] is the restriction of an element of [Formula: see text], unique up to the (finite) pointwise stabilizer of 𝔛 in [Formula: see text]. Furthermore, if S is not a twice-punctured torus, then we can replace [Formula: see text] in this statement with the extended mapping class group Mod ±(S).

Publisher

World Scientific Pub Co Pte Lt

Subject

Geometry and Topology,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793525313500076

Reference8 articles.

1. Curve Complexes and Finite Index Subgroups of Mapping Class Groups

2. The virtual cohomological dimension of the mapping class group of an orientable surface

3. Superinjective simplicial maps of complexes of curves and injective homomorphisms of subgroups of mapping class groups

4. Automorphisms of complexes of curves on punctured spheres and on punctured tori

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