Subgroups of Teichmuller Modular Groups (Translations of Mathematical Monographs) - Hardcover

Ivanov, Nikolai V.

Hardcover

ISBN 10: 0821845942 ISBN 13: 9780821845943

Publisher: Amer Mathematical Society, 1992

Synopsis

Teichmüller modular groups, also known as mapping class groups of surfaces, serve as a meeting ground for several branches of mathematics, including low-dimensional topology, the theory of Teichmüller spaces, group theory, and, more recently, mathematical physics. The present work focuses mainly on the group-theoretic properties of these groups and their subgroups. The technical tools come from Thurston's theory of surfaces---his classification of surface diffeomorphisms and the theory of measured foliations on surfaces. The guiding principle of this investigation is a deep analogy between modular groups and linear groups. For some of the central results of the theory of linear groups (such as the theorems of Platonov, Tits, and Margulis-Soifer), the author provides analogous results for the case of subgroups of modular groups. The results also include a clear geometric picture of subgroups of modular groups and their action on Thurston's boundary of Teichmüller spaces. Aimed at research mathematicians and graduate students, this book is suitable as supplementary material in advanced graduate courses.

About this title

Language Notes

Text: English
Original Language: Russian

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 1992
• ISBN 10: 0821845942
• ISBN 13: 9780821845943
• Binding: Hardcover
• Language: English
• Number of pages: 127