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Elliptic Curves and Modular Forms in Algebraic Topology

Proceedings of a Conference held at the Institute for Advanced Study, Princeton, Sept. 15-17, 1986

  • Conference proceedings
  • © 1988

Overview

Editors:
  1. Peter S. Landweber
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1326)

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About this book

A small conference was held in September 1986 to discuss new applications of elliptic functions and modular forms in algebraic topology, which had led to the introduction of elliptic genera and elliptic cohomology. The resulting papers range, fom these topics through to quantum field theory, with considerable attention to formal groups, homology and cohomology theories, and circle actions on spin manifolds. Ed. Witten's rich article on the index of the Dirac operator in loop space presents a mathematical treatment of his interpretation of elliptic genera in terms of quantum field theory. A short introductory article gives an account of the growth of this area prior to the conference.

Keywords

Table of contents (12 papers)

  1. Front Matter

    Pages I-V
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  2. Elliptic genera: An introductory overview

    • Peter S. Landweber
    Pages 1-10

  3. Elliptic formal groups over ℤ and F p in applications to number theory, computer science and topology

    • D. V. Chudnovsky, G. V. Chudnovsky
    Pages 11-54

  4. Elliptic cohomology and modular forms

    • Peter S. Landweber
    Pages 55-68

  5. Supersingular elliptic curves and congruences for legendre polynomials

    • Peter S. Landweber
    Pages 69-93

  6. Some weil group representations motivated by algebraic topology

    • Jack Morava
    Pages 94-106

  7. Genres elliptiques equivariants

    • Serge Ochanine
    Pages 107-122

  8. Complex cobordism theory for number theorists

    • Douglas C. Ravenel
    Pages 123-133

  9. Dirichlet series and homology theory

    • Larry Smith, R. E. Stong
    Pages 134-149

  10. Constrained Hamiltonians an introduction to homological algebra in field theoretical physics

    • James D. Stasheff
    Pages 150-160

  11. The index of the dirac operator in loop space

    • Edward Witten
    Pages 161-181

  12. Jacobi quartics, legendre polynomials and formal groups

    • Noriko Yui
    Pages 182-215

  13. Note on the Landweber-Stong elliptic genus

    • Don Zagier
    Pages 216-224

  14. Back Matter

    Pages 227-228
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Bibliographic Information

  • Book Title: Elliptic Curves and Modular Forms in Algebraic Topology

  • Book Subtitle: Proceedings of a Conference held at the Institute for Advanced Study, Princeton, Sept. 15-17, 1986

  • Editors: Peter S. Landweber

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0078035

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19490-3Published: 13 July 1988

  • eBook ISBN: 978-3-540-39300-9Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 232

  • Topics: Algebraic Topology, Theoretical, Mathematical and Computational Physics

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