O'Reilly logo

A Primer on Mapping Class Groups (PMS-49) by Dan Margalit, Benson Farb

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

line1

Overview

In this book we will consider two fundamental objects attached to a surface S: a group and a space. We will study these two objects and how they relate to each other.

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 diffeomorphisms of S (that restrict to the identity on ∂S if ∂Szeroslash):

Mod(S) = Diff+(S, ∂S) / Diff0(S, ∂S).

Here Diff0(S, ∂S) is the subgroup of Diff+(S, ∂S) consisting of elements that are isotopic to the identity. We will study ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required