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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". Iwanted to develop the theory of "Elliptic Genera" and to leam 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 Thom 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 Chem 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 o 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.
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Contenuti
Background.- Elliptic genera.- A universal addition theorem for genera.- Multiplicativity in fibre bundles.- The Atiyah-Singer index theorem.- Twisted operators and genera.- Riemann-Roch and elliptic genera in the complex case.- A divisibility theorem for elliptic genera.
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Book by Hirzebruch Friedrich
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Manifolds and Modular Forms, Vol. E20 (Aspects of Mathematics, E 20)
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Manifolds and Modular Forms Aspects of Mathematics 20 Aspects of Mathematics, E 20
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Manifolds and Modular Forms, Vol. E20 (Aspects of Mathematics, E 20)
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Manifolds and Modular Forms
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Taschenbuch. 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'. Iwanted to develop the theory of 'Elliptic Genera' and to leam 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 Thom 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 Chem 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 o 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. Deutsch. Codice articolo 9783528064143
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Manifolds and Modular Forms (Aspects of Mathematics)
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Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, 1992
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Background.- Elliptic genera.- A universal addition theorem for genera.- Multiplicativity in fibre bundles.- The Atiyah-Singer index theorem.- Twisted operators and genera.- Riemann-Roch and elliptic genera in the complex case.- A divisibility theorem for e. Codice articolo 4866905
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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'. Iwanted to develop the theory of 'Elliptic Genera' and to leam 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 Thom 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 Chem 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 o 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 9783528064143
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Manifolds and Modular Forms
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Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Jan 1992, 1992
ISBN 10: 3528064145
ISBN 13: 9783528064143
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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'. Iwanted to develop the theory of 'Elliptic Genera' and to leam 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 Thom 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 Chem 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 o 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. Deutsch. Codice articolo 9783528064143
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Manifolds and Modular Forms, Vol. E20 (Aspects of Mathematics, E 20)
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Manifolds and Modular Forms
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