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During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms". The A-genus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes.
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Contenuti
1 Background.- 2 Elliptic genera.- 3 A universal addition theorem for genera.- 4 Multiplicativity in fibre bundles.- 5 The Atiyah-Singer index theorem.- 6 Twisted operators and genera.- 7 Riemann-Roch and elliptic genera in the complex case.- 8 A divisibility theorem for elliptic genera.- Appendix I Modular forms.- 1 Fundamental concepts.- 2 Examples of modular forms.- 3 The Weierstraß ?-function as a Jacobi form.- 4 Some special functions and modular forms.- 5 Theta functions, divisors, and elliptic functions.- Appendix II The Dirac operator.- 1 The solution.- 2 The problem.- 1 Zolotarev polynomials.- 2 Interpretation as an algebraic curve.- 3 The differential equation — revisited.- 4 Modular interpretation of Zolotarev polynomials.- 5 The embedding of the modular curve.- 6 Applications to elliptic genera.- Symbols.
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Book by Hirzebruch Friedrich Berger Thomas Jung Rainer
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Manifolds and Modular Forms
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Vieweg+Teubner, Vieweg+Teubner Verlag Jan 1994, 1994
ISBN 10: 352816414X
ISBN 13: 9783528164140
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Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germania
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -During the winter term 1987/88 I gave a course at the University of Bonn under the title 'Manifolds and Modular Forms'. I wanted to develop the theory of 'Elliptic Genera' and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word 'genus' is meant in the sense of my book 'Neue Topologische Methoden in der Algebraischen Geometrie' published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the A-genus. The A-genus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the A-genus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the A-genus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold. 212 pp. Englisch. Codice articolo 9783528164140
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Manifolds and Modular Forms
Editore:
Vieweg Verlag, Friedr, & Sohn Verlagsgesellschaft mbH, 1994
ISBN 10: 352816414X
ISBN 13: 9783528164140
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Condizione: New. pp. xi + 2nd Edition. Codice articolo 26142280698
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Manifolds and Modular Forms
Editore:
Vieweg Verlag, Friedr, & Sohn Verlagsgesellschaft mbH, 1994
ISBN 10: 352816414X
ISBN 13: 9783528164140
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Condizione: New. Print on Demand pp. xi +. Codice articolo 135051301
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Manifolds and Modular Forms
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Vieweg Verlag, Friedr, & Sohn Verlagsgesellschaft mbH, 1994
ISBN 10: 352816414X
ISBN 13: 9783528164140
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Da: Biblios, Frankfurt am main, HESSE, Germania
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Condizione: New. PRINT ON DEMAND pp. xi +. Codice articolo 18142280688
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book provides a comprehensive introduction to the theory of elliptic genera due to Ochanine, Landweber, Stong, and others. The theory describes a new cobordism invariant for manifolds in terms of modular forms. The book evolved from notes of a course . Codice articolo 4867639
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Manifolds and Modular Forms (Aspects of Mathematics)
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Paperback. Condizione: Brand New. 2nd edition. 223 pages. 9.00x6.25x0.75 inches. In Stock. Codice articolo 352816414X
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Manifolds and Modular Forms
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Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Jan 1994, 1994
ISBN 10: 352816414X
ISBN 13: 9783528164140
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Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germania
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Taschenbuch. Condizione: Neu. Neuware -During the winter term 1987/88 I gave a course at the University of Bonn under the title 'Manifolds and Modular Forms'. I wanted to develop the theory of 'Elliptic Genera' and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word 'genus' is meant in the sense of my book 'Neue Topologische Methoden in der Algebraischen Geometrie' published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the A-genus. The A-genus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the A-genus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the A-genus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold.Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Straße 46, 65189 Wiesbaden 228 pp. Englisch. Codice articolo 9783528164140
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Manifolds and Modular Forms
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - During the winter term 1987/88 I gave a course at the University of Bonn under the title 'Manifolds and Modular Forms'. I wanted to develop the theory of 'Elliptic Genera' and to learn it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word 'genus' is meant in the sense of my book 'Neue Topologische Methoden in der Algebraischen Geometrie' published in 1956: A genus is a homomorphism of the Thorn cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the A-genus. The A-genus equals the arithmetic genus of an algebraic manifold, provided the first Chern class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the A-genus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps 0 giving the signature and the A-genus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold. Codice articolo 9783528164140
Quantità: 1 disponibili
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Manifolds and Modular Forms
Editore:
Vieweg+Teubner Verlag, 1994
ISBN 10: 352816414X
ISBN 13: 9783528164140
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Da: Buchpark, Trebbin, Germania
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Condizione: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher. Codice articolo 23163618/202
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