Moduli Spaces of Curves, Mapping Class Groups and Field Theory - Softcover

Softcover

ISBN 10: 0821831674 ISBN 13: 9780821831670

Publisher: Amer Mathematical Society, 2003

Synopsis

This book grew out of a workshop on the applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations. Chapter 1 gives an introduction to Teichmuller space that is more concise than the popular textbooks, yet contains full proofs of many useful results which are often difficult to find in the literature. This chapter also contains an introduction to moduli spaces of curves, with a detailed description of the genus zero case, and in particular of the part at infinity. Chapter 2 takes up the subject of the genus zero moduli spaces and gives a complete description of their fundamental groupoids, based at tangential base points neighboring the part at infinity; the description relies on an identification of the structure of these groupoids with that of certain canonical subgroupoids of a free braided tensor category. It concludes with a study of the canonical Galois action on the fundamental groupoids, computed using Grothendick-Teichmuller theory. Finally, Chapter 3 studies strict ribbon categories, which are closely related to braided tensor categories: here they are used to construct invariants of 3-manifolds which in turn give rise to quantum field theories.

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 2003
• Language: English
• ISBN 10: 0821831674
• ISBN 13: 9780821831670
• Binding: Paperback
• Number of pages: 131
• Editor: Buff Xavier, Fehrenbach Jerome, Lochak Pierre, Schneps Leila, Vogel Pierre