Mapping class group

Mapping class group ... In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space.

A Brief Introduction to Mapping Class Groups - Yale Math

My job was to introduce the mapping class group of a surface, discuss its basic features from a topologist's point of view, and give a description of the ...

Mapping class group of a surface - Wikipedia

The mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up ...

A Primer on Mapping Class Groups

The group. The group is the mapping class group of S, denoted by. Mod(S). It is defined to be the group of isotopy classes of orientation- preserving ...

AN INTRODUCTION TO MAPPING CLASS GROUPS OF SURFACES

Let S be a closed orientable surface of genus g ≥ 1. The mapping class group of S, denoted by Mod(Sg), is the group of isotopy classes of orientation-preserving ...

I will be giving an introductory talk on mapping class groups ... - Reddit

One key property of mapping class groups is that they are finitely generated. This means that they can be represented as a group generated by a ...

mapping class group in nLab

The mapping class group is of importance in many areas of geometry including study of Teichmüller spaces, of moduli spaces of surfaces, of ...

Mapping class groups - DPMMS

Mod(S). SLn(Z) mapping classes linear maps closed curves on S vectors in Zn ... ... Lecture 2: Surfaces and hyperbolic geometry. A closed curve on a surface S ...

Mapping class groups: the next generation

A beautiful new paper by Juliette Bavard which opens up a dramatic new range of applications of ideas from the classical theory of mapping class groups.

[2003.07950] Big mapping class groups: an overview - arXiv

Authors:Javier Aramayona, Nicholas G. Vlamis View PDF Abstract:We survey recent developments on mapping class groups of surfaces of infinite topological type.

Current status of the linearity of mapping class group - MathOverflow

The authors provide a faithful linear-categorical action of the mapping class group of a surface with necessarily non-empty boundary using knot Floer homology.

Motivation for the Mapping Class Group - Math Stack Exchange

A couple of things spring to mind. One is that if you are interested in 3-manifolds, then the study of the mapping class group is the most ...

A short introduction to mapping class groups - of Gwénaël Massuyeau

We introduce the mapping class group of a surface and its enigmating subgroup, the Torelli group. One hour and seventeen pages are certainly not enough to ...

The mapping class group from the viewpoint of measure ... - arXiv

We obtain some classification result for the mapping class groups of compact orientable surfaces in terms of measure equivalence.

An Introduction to Mapping Class Groups

Mapping class group: MCG(S) = Homeo+(S)/ ∼ f ∼ g if f and g are isotopic. The mapping class group is a countable group, in fact it is finitely.

A simple presentation for the mapping class group of an orientable ...

LetF n.k be an orientable compact surface of genusn withk boundary components. For a suitable choice of 2n + 1 simple closed curves onF n,1 the correspondi.

BIG MAPPING CLASS GROUPS: AN OVERVIEW

Calegari proposed the study of the mapping class group Map(R2 \C), where C denotes a Cantor set. More concretely, he posed the question of whether this group ...

Motives and mapping class groups | American Inst. of Mathematics

Motives and mapping class groups ... This workshop, sponsored by AIM and the NSF, will bring together experts to investigate the dynamics of character varieties ...

Studying the mapping class group of a surface through its actions

... mapping class group of closed surfaces. Theorem 2.1 (Dehn-Nielsen-Baer). If S = Sg is a closed surface with genus g > 0, then the group homomorphism Γ±. S ...

Problems on Mapping Class Groups and Related Topics

... mapping class group and beyond. S. Morita. 350. Chapter 23. From braid groups to mapping class groups. L. Paris. 379. Page 6. Preface. The study of mapping ...