Moduli Spaces of Curves

Moduli Spaces of Curves

by X. Buff, Pie Vogel, Pierre Lochak, Pierre Vogel
     
 

ISBN-10: 0821831674

ISBN-13: 9780821831670

Pub. Date: 06/28/2003

Publisher: American Mathematical Society

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

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Overview

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 Grothendieck-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.

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Product Details

ISBN-13:
9780821831670
Publisher:
American Mathematical Society
Publication date:
06/28/2003
Series:
SMF/AMS Texts and Monographs, #9
Pages:
131

Table of Contents

Preface
Ch. 1Elements of the geometry of moduli spaces of curves1
Ch. 2Fundamental groupoids of genus zero moduli spaces and braided tensor categories59
Ch. 3Witten-Reshetikhin-Turaev Invariants and Quantum Field Theories105

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