UID:
almafu_9959234303902883
Format:
1 online resource (xiv, 364 pages) :
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digital, PDF file(s).
ISBN:
1-139-88269-4
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1-107-36788-3
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1-107-37242-9
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1-107-36297-0
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1-107-36881-2
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1-299-40548-7
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1-107-36542-2
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0-511-89386-8
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0-511-72148-X
Series Statement:
London Mathematical Society lecture note series ; 342
Content:
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.
Note:
"[Papers from] a workshop entitled 'Elliptic Cohomology and Chromatic Phenomena' ... held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, on 9-20 December, 2002"--Pref.
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Cover; Title; Copyright; Contents; Preface; Charles Thomas, 1938-2005; 1. Discrete torsion for the supersingular orbifold sigma genus; 1. Introduction; 1. Introduction; 2. The sigma orientation and the sigma genus; 2. The sigma orientation and the sigma genus; 3. The sigma genus; 3. The sigma genus; 4. The Borel-equivariant sigma genus; 4. The Borel-equivariant sigma genus; 5. Character theory; 5. Character theory; 6. The orbifold sigma genus; 6. The orbifold sigma genus; 7. Comparison with the analytic equivariant genus; 7. Comparison with the analytic equivariant genus; 8. The cocycle
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8. The cocycle9. Discrete torsion; 9. Discrete torsion; 10. The non-abelian Case; 10. The non-abelian Case; References; References; 2. Quaternionic elliptic objects and K3-cohomology; 3. The M-theory 3-form and E8 gauge theory; 1. Introduction; 2. The gauge equivalence class of a C-field; 3. Models for the C-field; 4. The definition of the C-field measure for Y without boundary; 5. The C-field measure when Y has a boundary; 6. The action of the gauge group on the physical wavefunction and the Gauss law; 7. The definition of C-field electric charge; 8. Mathematical Properties of ΘX(Č)
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9. Φ as a cubic refinement, with applications to integration over flat C-fields10. Application 1: The 5-brane partition function; 11. Application 2: Relation of M-theory to K-theory; 12. Application 3: Comments on spatial boundaries; 13. Conclusions and future directions; References; 4. Algebraic groups and equivariant cohomology theories; Contents; 1. Introduction.; 2. K-theory and the multiplicative group.; 3. The shape of a cohomology theory.; 4. The non-split torus.; 5. Elliptic cohomology and elliptic curves.; 6. T-equivariant elliptic cohomology.; 7. Shapes from projective varieties.
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3.1 Explicit examples III3.2 The general problem; 3.3 Explicit examples IV: the case n = 2 and p = 3; 3.4 Work in progress (the case n = p = 2); 3.5 Permutation resolutions in the case n = k(p-1) for p odd.; 3.6 Resolutions for LK(n)S0 for p odd and n = p-1.; Appendix: Splitting En with respect to the action of F n(q -1); References; 7. Chromatic phenomena in the algebra of BP*BP-comodules; Introduction; 1. Comodules; 2. Landweber exact algebras; 3. The stable homotopy category Stable(Г); 4. Landweber exactness and the stable homotopy category; References
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8. Numerical polynomials and endomorphisms of formal group laws
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English
Additional Edition:
ISBN 0-521-70040-X
Language:
English
Subjects:
Mathematics
Keywords:
Konferenzschrift
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Konferenzschrift
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Festschrift
URL:
https://doi.org/10.1017/CBO9780511721489
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