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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...

Autorul evidentiaza o serie de aspecte, adesea neglijate, cu care se confrunta mediul educational romanesc in prezent, printre care si rolul central al gandirii, intelegerii in inv...

This chapter focuses on the moduli space of Riemann surfaces. The moduli space parameterizes many different kinds of structures on Sɡ, such as isometry classes of hyperbolic struct...