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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
 
Xavier Buff Université Paul Sabatier, Toulouse, France
Jérôme Fehrenbach University of Nice Sophia-Antipolis, Valbonne, France
Pierre Lochak Centre de Mathématiques de Jussieu, Université Paris VI, Paris, France
Leila Schneps Université Paris VI, Paris, France
Pierre Vogel Université Paris VII, Paris, France
A co-publication of the AMS and the Société Mathématique de France
Moduli Spaces of Curves, Mapping Class Groups and Field Theory
Softcover ISBN:  978-0-8218-3167-0
Product Code:  SMFAMS/9
List Price: $58.00
MAA Member Price: $52.20
AMS Member Price: $46.40
Moduli Spaces of Curves, Mapping Class Groups and Field Theory
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
Xavier Buff Université Paul Sabatier, Toulouse, France
Jérôme Fehrenbach University of Nice Sophia-Antipolis, Valbonne, France
Pierre Lochak Centre de Mathématiques de Jussieu, Université Paris VI, Paris, France
Leila Schneps Université Paris VI, Paris, France
Pierre Vogel Université Paris VII, Paris, France
A co-publication of the AMS and the Société Mathématique de France
Softcover ISBN:  978-0-8218-3167-0
Product Code:  SMFAMS/9
List Price: $58.00
MAA Member Price: $52.20
AMS Member Price: $46.40
  • Book Details
     
     
    SMF/AMS Texts and Monographs
    Volume: 92003; 131 pp
    MSC: Primary 32; 20; 11;

    This is a collection of articles that grew out of a workshop organized to discuss deep links among various topics that were previously considered unrelated. Rather than a typical workshop, this gathering was unique as it was structured more like a course for advanced graduate students and research mathematicians.

    In the book, the authors present 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 Teichmüller 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-Teichmüller 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. The material is suitable for advanced graduate students and researchers interested in algebra, algebraic geometry, number theory, and geometry and topology.

    Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.

    Readership

    Advanced graduate students and researchers interested in algebra, algebraic geometry, number theory, and geometry and topology.

  • Additional Material
     
     
  • Reviews
     
     
    • From a review of the French edition:

      A collective monograph dedicated to the new and profound relations between various theories previously considered as unrelated ... A specific feature of the book, which distinguishes it from many other monographs and textbooks on the same subjects, is its nature of a ‘guide for the non-specialist’ ... it also contains full proofs of some results difficult to find elsewhere ... Examples are studied in great detail ... Recommended as a first reading for a non-specialist who wants to get acquainted with the subject but who does not want to get lost in its many intricacies and ramifications.

      Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 92003; 131 pp
MSC: Primary 32; 20; 11;

This is a collection of articles that grew out of a workshop organized to discuss deep links among various topics that were previously considered unrelated. Rather than a typical workshop, this gathering was unique as it was structured more like a course for advanced graduate students and research mathematicians.

In the book, the authors present 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 Teichmüller 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-Teichmüller 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. The material is suitable for advanced graduate students and researchers interested in algebra, algebraic geometry, number theory, and geometry and topology.

Titles in this series are co-published with Société Mathématique de France. SMF members are entitled to AMS member discounts.

Readership

Advanced graduate students and researchers interested in algebra, algebraic geometry, number theory, and geometry and topology.

  • From a review of the French edition:

    A collective monograph dedicated to the new and profound relations between various theories previously considered as unrelated ... A specific feature of the book, which distinguishes it from many other monographs and textbooks on the same subjects, is its nature of a ‘guide for the non-specialist’ ... it also contains full proofs of some results difficult to find elsewhere ... Examples are studied in great detail ... Recommended as a first reading for a non-specialist who wants to get acquainted with the subject but who does not want to get lost in its many intricacies and ramifications.

    Mathematical Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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