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Document Type: Book
All Authors / Contributors: Friedrich Hirzebruch; Thomas Berger; Rainer Jung; Peter S Landweber; Max-Planck-Institut für Mathematik.
ISBN: 352816414X 9783528164140
OCLC Number: 438875785
Description: XII, 211 str.
Contents: 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.
Series Title: Aspects of mathematics, vol. E 20.
Responsibility: Friedrich Hirzebruch, Thomas Berger, Reiner Jung ; translated by Peter S. Landweber.

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