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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.
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
Editore:
American Mathematical Society, US, 2003
ISBN 10: 0821831674
ISBN 13: 9780821831670
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Paperback. Condizione: New. 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. Codice articolo LU-9780821831670
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory.
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ISBN 10: 0821831674
ISBN 13: 9780821831670
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Softcover. Condizione: Sehr gut. Providence, AMS (2003). 4°. VIII, 131 p. Pbck. SMF/AMS Texts and Monographs, 9. Codice articolo 96158
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
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Condizione: New. Presents applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations. This book gives an introduction to Teichmuller space and to moduli spaces of curves, with a description of the genus zero case, and in particular of the part at infinity. Series: SMF/AMS Texts & Monographs. Num Pages: 131 pages, Illustrations, 1 port. BIC Classification: PBG; PBH; PBKD; PBM. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 230. Weight in Grams: 283. . 2003. Paperback. . . . . Codice articolo V9780821831670
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
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Condizione: New. Presents applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations. This book gives an introduction to Teichmuller space and to moduli spaces of curves, with a description of the genus zero case, and in particular of the part at infinity. Series: SMF/AMS Texts & Monographs. Num Pages: 131 pages, Illustrations, 1 port. BIC Classification: PBG; PBH; PBKD; PBM. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 230. Weight in Grams: 283. . 2003. Paperback. . . . . Books ship from the US and Ireland. Codice articolo V9780821831670
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
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American Mathematical Society, 2003
ISBN 10: 0821831674
ISBN 13: 9780821831670
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
Editore:
American Mathematical Society, US, 2003
ISBN 10: 0821831674
ISBN 13: 9780821831670
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Paperback. Condizione: New. 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. Codice articolo LU-9780821831670
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Moduli Spaces of Curves, Mapping Class Groups and Field Theory
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ISBN 10: 0821831674
ISBN 13: 9780821831670
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