Moduli Spaces of Curves, Mapping Class Groups and Field Theory

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9780821831670: Moduli Spaces of Curves, Mapping Class Groups and Field Theory

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 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. The material is suitable for advanced graduate students and researchers interested in algebra, algebraic geometry, number theory, and geometry and topology.

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Xavier Buff, Jerome Fehrenbach, Pierre Lochak
Published by American Mathematical Society, United States (2003)
ISBN 10: 0821831674 ISBN 13: 9780821831670
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Book Description American Mathematical Society, United States, 2003. Paperback. Book Condition: New. Language: English . Brand New Book. 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 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. The material is suitable for advanced graduate students and researchers interested in algebra, algebraic geometry, number theory, and geometry and topology. Bookseller Inventory # AAN9780821831670

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Xavier Buff, Jerome Fehrenbach, Pierre Lochak
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Book Description American Mathematical Society, United States, 2003. Paperback. Book Condition: New. Language: English . Brand New Book. 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 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. The material is suitable for advanced graduate students and researchers interested in algebra, algebraic geometry, number theory, and geometry and topology. Bookseller Inventory # AAN9780821831670

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Book Description American Mathematical Society. Paperback. Book Condition: New. New copy - Usually dispatched within 2 working days. Bookseller Inventory # B9780821831670

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Book Description Amer Mathematical Society, 2003. Paperback. Book Condition: New. book. Bookseller Inventory # M0821831674

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Buff, Xavier (Editor)/ Fehrenbach, Jerome (Editor)/ Lochak, Pierre (Editor)/ Schneps, Leila (Editor)/ Vogel, Pierre (Editor)
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Book Description Amer Mathematical Society, 2003. Paperback. Book Condition: Brand New. illustrated edition. 131 pages. 9.75x6.75x0.25 inches. In Stock. Bookseller Inventory # __0821831674

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Editor-Xavier Buff; Editor-Jerome Fehrenbach; Editor-Pierre Lochak; Editor-Leila Schneps; Editor-Pierre Vogel
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Book Description Amer Mathematical Society, 2003. Paperback. Book Condition: New. Bookseller Inventory # SONG0821831674

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Xavier Buff (Editor), Jerome Fehrenbach (Editor), Pierre Lochak (Editor), Leila Schneps (Editor), Pierre Vogel (Editor)
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