Simplicial actions of mapping class groups
type: Dataset
description: In this chapter, we review the actions of the (extended) mapping class group of a surface of finite type by simplicial automorphisms on various abstract simplicial complexes (the curve complex, the arc complex, the cut system complex, the pants decomposition complex, the ideal triangulation complex, etc.). Each of these complexes has some special combinatorial features, and there are interesting questions that are particular to each one. We study in detail the actions on recently defined complexes, namely, the complex of domains and some of its subcomplexes. In most cases mentioned, the automorphism group of the simplicial automorphism coincides with the (injective) image of the mapping class group in that automorphism group. In the case of the complex of domains, this does not hold, as soon as the surface has at least two boundary components. We compute the automorphism group of the complex of domains, and we introduce a subcomplex of this complex, the truncated complex of domains, whose automorphism group is the extended mapping class group. The survey contains expository sections on surfaces and related objects and on simplicial complexes.
landing page: Handbook of Teichmüller theory, Volume III
identifier: ISBN: 978-3-03719-103-3
keyword: 57m99--30f99--57m60--57m50--20f65--57n05
keyword: arc-and-curve-complex
keyword: arc-complex
keyword: book-sections
keyword: boundary-graph-complex
keyword: complex-of-domains
keyword: complex-of-nonseparating-curves
keyword: complex-of-separating-curves
keyword: curve-complex
keyword: cut-system
keyword: exchange-automorphism
keyword: ideal-triangulation
keyword: infoeu-reposemanticsbookpart
keyword: mapping-class-group
keyword: mathmath-gtmathematics-mathgeometric-topology-mathgt
keyword: pants-decomposition
keyword: simplicial-automorphism
keyword: simplicial-complex
keyword: surface
keyword: torelli-complex
keyword: truncate-complex-of-domains
issued: 2026-05-15T19:09:14.826455
modified: 2026-05-15T19:09:14.826460
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Simplicial actions of mapping class groups
type: Distribution
format: HTML
access URL: https://hal.science/hal-00707476
issued: 2026-05-15T19:09:14.925582
modified: 2026-05-15T19:09:14.790885