Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
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.
Product Description
Book by Hirzebruch Friedrich Berger Thomas Jung Rainer
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Manifolds and Modular Forms
Editore:
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
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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
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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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ISBN 10: 352816414X
ISBN 13: 9783528164140
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Condizione: New. PRINT ON DEMAND pp. xi +. Codice articolo 18142280688
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Manifolds and Modular Forms. Translated by Peter S. Landweber. A Publication from the Max-Planck-Institut für Mathematik, Bonn.
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Braunschweig, Wiesbaden: Verlag Friedrich Vieweg & Sohn, 1994
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ISBN 13: 9783528164140
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Second Edition. XI, 211 Seiten, Format 16 x 23 cm, hartgebundener u. glanzkaschierter Original-Pappband (Reihe: Aspects of Mathematics). * Bibliography + Index auf den Seiten 199-207. Erhaltung: Auf dem rückseitigen Deckel ein Preis-Etikett (DM 74,00). Sonst keine weiteren Mängel und insgesamt sehr gut erhalten [Eine größere Sammlung Physik, Mathematik, Astronomie und verwandte Gebiete wird derzeit in den Bestand eingearbeitet. Sie finden diese Titel bei uns in den gleichnamigen Rubriken]. Sprache: Englisch. Codice articolo 29692
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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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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
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Vieweg+Teubner Verlag, Vieweg+Teubner Verlag Jan 1994, 1994
ISBN 10: 352816414X
ISBN 13: 9783528164140
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. 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.Vieweg+Teubner Verlag, Abraham-Lincoln-Straße 46, 65189 Wiesbaden 228 pp. Englisch. Codice articolo 9783528164140
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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
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Taschenbuch. Condizione: Neu. Manifolds and Modular Forms | Friedrich Hirzebruch (u. a.) | Taschenbuch | Aspects of Mathematics | xi | Englisch | 1994 | Vieweg & Teubner | EAN 9783528164140 | Verantwortliche Person für die EU: Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Str. 46, 65189 Wiesbaden, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Codice articolo 102478089
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