Elliptic Cohomology
Geometry, Applications, and Higher Chromatic Analogues

First collection of papers on elliptic cohomology in twenty years; represents the diversity of topics within this important field.

Haynes R. Miller (Edited by), Douglas C. Ravenel (Edited by)

9780521700405, Cambridge University Press

Paperback, published 15 March 2007

380 pages, 3 exercises
22.9 x 15.4 x 2 cm, 0.537 kg

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.

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.

Subject Areas: Mathematical physics [PHU], Applied mathematics [PBW], Topology [PBP], Geometry [PBM]