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Distortion and Tits alternative in smooth mapping class groups
- Source :
- Transactions of the American Mathematical Society, Transactions of the American Mathematical Society, American Mathematical Society, 2019, 371 (12), pp.8587-8623
- Publication Year :
- 2015
- Publisher :
- arXiv, 2015.
-
Abstract
- In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve this Cantor set. When the Cantor set is the standard ternary Cantor set, we prove that the subgroup consisting of diffeomorphisms which are isotopic to the identity on S does not contain any distorted elements. Moreover, we prove a weak Tits alternative for these groups.<br />Comment: Theorem 1.1. has been improved in this version
- Subjects :
- Pure mathematics
Class (set theory)
Tits alternative
Mathematics::Dynamical Systems
General Mathematics
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
Mathematics::General Topology
Dynamical Systems (math.DS)
Group Theory (math.GR)
01 natural sciences
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
Mathematics - Geometric Topology
[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]
FOS: Mathematics
0101 mathematics
Mathematics - Dynamical Systems
MSC 37C85, 57S25
Mathematics
Group (mathematics)
Applied Mathematics
010102 general mathematics
Geometric Topology (math.GT)
Surface (topology)
Mapping class group
Distortion (mathematics)
Cantor set
Mathematics::Logic
Isotopy
Mathematics - Group Theory
Subjects
Details
- ISSN :
- 00029947
- Database :
- OpenAIRE
- Journal :
- Transactions of the American Mathematical Society, Transactions of the American Mathematical Society, American Mathematical Society, 2019, 371 (12), pp.8587-8623
- Accession number :
- edsair.doi.dedup.....9ba4255148710e5875f0c3d683b00f02
- Full Text :
- https://doi.org/10.48550/arxiv.1506.02877