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This book deals with two fundamental objects attached to a surface S and how they relate to each other: a group and a space. The group is the mapping class group of S, denoted by M...

This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the...

This chapter discusses the basic properties and applications of a symplectic representation, denoted by Ψ‎, and its kernel, called the Torelli group. After describing the algebraic...

This chapter deals with Dehn twists, the simplest infinite-order elements of Mod(S). It first defines Dehn twists and proves that they are nontrivial elements of the mapping class ...

This chapter deals with finite subgroups of the mapping class group. It first explains the distinction between finite-order mapping classes and finite-order homeomorphisms, focusin...

Essential Cases: Tort Law provides a bridge between course textbooks and key case judgments. This case document summarizes the facts and decision in Tuberville v Savage (1669) 1 Mo...