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Elliptic Cohomology

Elliptic Cohomology
Geometry, Applications, and Higher Chromatic Analogues

Part of London Mathematical Society Lecture Note Series

Matthew Ando, Christopher P. French, Jorge A. Devoto, John P. C. Greenlees, Ian Grojnowski, Hans-Werner Henn, Mark Hovey, Keith Johnson, Nitu Kitchloo, Jack Morava, Geoffrey Mason, Norihiko Minami, Emanuel Diaconescu, Daniel S. Freed, Gregory Moore, Douglas C. Ravenel, Graeme Segal, Bertrand Toen, Gabriele Vezzosi, Burt Totaro
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  • Date Published: May 2007
  • availability: Available
  • format: Paperback
  • isbn: 9780521700405

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About the Authors
  • Edward Witten once said that Elliptic Cohomology was a piece of 21st Century Mathematics that happened to fall into the 20th Century. He also likened our understanding of it to what we know of the topography of an archipelago; the peaks are beautiful and clearly connected to each other, but the exact connections are buried, as yet invisible. This very active subject has connections to algebraic topology, theoretical physics, number theory and algebraic geometry, and all these connections are represented in the sixteen papers in this volume. A variety of distinct perspectives are offered, with topics including equivariant complex elliptic cohomology, the physics of M-theory, the modular characteristics of vertex operator algebras, and higher chromatic analogues of elliptic cohomology. This is the first collection of papers on elliptic cohomology in almost twenty years and gives a broad picture of the state of the art in this important field of mathematics.

    • Presents the current state of the art in elliptic cohomology
    • First collection of papers on this subject for 20 years
    • Ideal for graduate students and researchers in topology, algebraic geometry, representation theory and string theory
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    Product details

    • Date Published: May 2007
    • format: Paperback
    • isbn: 9780521700405
    • length: 380 pages
    • dimensions: 229 x 154 x 20 mm
    • weight: 0.537kg
    • contains: 3 exercises
    • availability: Available
  • Table of Contents

    Preface
    1. Discrete torsion for the supersingular orbifold sigma genus Matthew Ando and Christopher P. French
    2. Quaternionic elliptic objects and K3-cohomology Jorge A. Devoto
    3. Algebraic groups and equivariant cohomology theories John P. C. Greenlees
    4. Delocalised equivariant elliptic cohomology Ian Grojnowski
    5. On finite resolutions of K(n)-local spheres Hans-Werner Henn
    6. Chromatic phenomena in the algebra of BP*BP-comodules Mark Hovey
    7. Numerical polynomials and endomorphisms of formal group laws Keith Johnson
    8. Thom prospectra for loopgroup representations Nitu Kitchloo and Jack Morava
    9. Rational vertex operator algebras Geoffrey Mason
    10. A possible hierarchy of Morava K-theories Norihiko Minami
    11. The M-theory 3-form and E8 gauge theory Emanuel Diaconescu, Daniel S. Freed and Gregory Moore
    12. The motivic Thom isomorphism Jack Morava
    13. Toward higher chromatic analogs of elliptic cohomology Douglas C. Ravenel
    14. What is an elliptic object? Graeme Segal
    15. Spin cobordism, contact structure and the cohomology of p-groups C. B. Thomas
    16. Brave New Algebraic Geometry and global derived moduli spaces of ring spectra Bertrand Toen and Gabriele Vezzosi
    17. The elliptic genus of a singular variety Burt Totaro.

  • Editors

    Haynes R. Miller, Massachusetts Institute of Technology
    Haynes C. Miller is Professor of Mathematics at Massachusetts Institute of Technology, Boston.

    Douglas C. Ravenel, University of Rochester, New York
    Douglas C. Ravenel is Fayerweather Professor of Mathematics, University of Rochester, NY.

    Contributors

    Matthew Ando, Christopher P. French, Jorge A. Devoto, John P. C. Greenlees, Ian Grojnowski, Hans-Werner Henn, Mark Hovey, Keith Johnson, Nitu Kitchloo, Jack Morava, Geoffrey Mason, Norihiko Minami, Emanuel Diaconescu, Daniel S. Freed, Gregory Moore, Douglas C. Ravenel, Graeme Segal, Bertrand Toen, Gabriele Vezzosi, Burt Totaro

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