A primer on mapping class groups
@inproceedings{Farb2013APO,
title={A primer on mapping class groups},
author={Benson Farb and Danielle N Margalit},
year={2013}
}Given a compact connected orientable surface S there are two fundamental objects attached: a group and a space. The group is the mapping class group of S, denoted by Mod(S). This group is defined by the isotopy classes of orientation-preserving homeomorphism from S to itself. Equivalently, Mod(S) may be defined using diffeomorphisms instead of homeomorphisms or homotopy classes instead of isotopy classes. The space is the Teichmüller space of S, Teich(S). Teichmüller space and moduli space are…
Figures from this paper
figure 1 
figure 1.1 
figure 1.2 
figure 1.3 
figure 1.4 
figure 1.5 
figure 1.6 
figure 1.7 
figure 1.8 
figure 2.1 
figure 2.10 
figure 2.2 
figure 2.3 
figure 2.4 
figure 2.5 
figure 2.6 
figure 2.7 
figure 2.8 
figure 2.9 
figure 3.1 
figure 3.2 
figure 3.3 
figure 3.4 
figure 3.5 
figure 3.6 
figure 3.7 
figure 3.8 
figure 3.9 
figure 4.1 
figure 4.10 
figure 4.11 
figure 4.2 
figure 4.3 
figure 4.4 
figure 4.5 
figure 4.6 
figure 4.7 
figure 4.8 
figure 4.9 
figure 5.1 
figure 5.10 
figure 5.11 
figure 5.12 
figure 5.13 
figure 5.2 
figure 5.3 
figure 5.4 
figure 5.5 
figure 5.6 
figure 5.7 
figure 5.8 
figure 5.9 
figure 6.1 
figure 6.2 
figure 6.3 
figure 6.4 
figure 6.5 
figure 7.1 
figure 8.1 
figure 8.2 
figure 9.1 
figure 9.10 
figure 9.12 
figure 9.13 
figure 9.14 
figure 9.15 
figure 9.2 
figure 9.3 
figure 9.4 
figure 9.5 
figure 9.6 
figure 9.7 
figure 9.8 
figure 9.9 
figure 10.1 
figure 10.10 
figure 10.11 
figure 10.2 
figure 10.3 
figure 10.4 
figure 10.5 
figure 10.6 
figure 10.7 
figure 10.8 
figure 10.9 
figure 11.1 
figure 11.10 
figure 11.11 
figure 11.2 
figure 11.3 
figure 11.4 
figure 11.5 
figure 11.6 
figure 11.7 
figure 11.8 
figure 11.9 
figure 12.1 
figure 12.2 
figure 12.3 
figure 13.1 
figure 13.2 
figure 13.3 
figure 13.4 
figure 14.1 
figure 14.2 
figure 14.3 
figure 14.4 
figure 14.5 
figure 14.6 
figure 15.1 
figure 15.10 
figure 15.11 
figure 15.12 
figure 15.13 
figure 15.14 
figure 15.15 
figure 15.16 
figure 15.17 
figure 15.2 
figure 15.3 
figure 15.4 
figure 15.5 
figure 15.6 
figure 15.7 
figure 15.8 
figure 15.9
1,345 Citations
TOPIC PROPOSAL THE MAPPING CLASS GROUP AND THE MODULI SPACE OF RIEMANN SURFACES
- Mathematics
- 2014
Closed surfaces are completely classified by Euler characteristic. The next natural step is to study maps between surfaces. Two important classes of maps to be studied are homeomorphisms and finite…
Point-pushing actions for manifolds with boundary
- Mathematics
- 2020
Given a manifold M and a point in its interior, the point-pushing map describes a diffeomorphism that pushes the point along a closed path. This defines a homomorphism from the fundamental group of M…
DEFORMATIONS OF SURFACES EMBEDDED IN THE 4-DIMENSIONAL MANIFOLDS AND THEIR MAPPING CLASS GROUPS
- Mathematics
- 2013
In many researches on geometric topology, we can find discussions on a surface which is a submanifold of some manifold. There are two way to think about this surface, (1) regard it just as a subset…
Asymptotic mapping class groups of Cantor manifolds and their finiteness properties
- Mathematics
- 2021
A Cantor manifold C is a non-compact manifold obtained by gluing (holed) copies of a fixed compact manifold Y in a tree-like manner. Generalizing classical families of groups due to Brin [10],…
Nielsen realization for infinite-type surfaces
- Mathematics
- 2020
Given a finite subgroup G of the mapping class group of a surface S, the Nielsen realization problem asks whether G can be realized as a finite group of homeomorphisms of S. In 1983, Kerckhoff showed…
The symplectic representation of the mapping class group is surjective
- Mathematics
- 2018
We give an efficient proof that the symplectic representation of the mapping class group is surjective. Let Σg be a closed oriented genus g surface and let Modg be its mapping class group, that is,…
The dynamics of mapping classes on surfaces
- Mathematics
- 2011
Let M be a hyperbolic 3-manifold. Let φ : S → S be a pseudo-Anosov mapping class such that M = Mφ is the mapping torus. We have seen that there is a fibered face F ⊂ H1(M ;R) so that φ is the…
The space of metric structures on hyperbolic groups
- Mathematics
- 2022
. We study the metric and topological properties of the space D p G q of left-invariant hyperbolic metrics on the non-elementary hyperbolic group G that are quasi-isometric to a word metric, up to…
Thurston's Work on Surfaces
- Mathematics
- 2012
This book is an exposition of Thurston’s theory of surfaces: measured foliations, the compactification of Teichmuller space and the classification of diffeomorphisms. The mathematical content is…
References
Mappings (Mathematics) 2. Class groups
- PM To Amie and Kathleen Unauthenticated Download
- 2011