Manifolds and Modular Forms

Jung Rainer Berger Thomas Hirzebruch Friedrich

ISBN 10: 352816414X / ISBN 13: 9783528164140

Editore: Vieweg Verlag, Friedr, & Sohn Verlagsgesellschaft mbH, 1994

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Codice articolo 18142280688

Dati bibliografici

• Titolo: Manifolds and Modular Forms
• Editore: Vieweg Verlag, Friedr, & Sohn Verlagsgesellschaft mbH
• Data di pubblicazione: 1994
• Lingua: Inglese
• ISBN 10: 352816414X
• ISBN 13: 9783528164140
• Rilegatura: Brossura
• Edizione: seconda edizione
• Condizione: New

Descrizione articolo

Riassunto

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.

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.