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.
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| Otros Autores: | , |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press
2007.
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| Colección: | EBSCO Academic eBook Collection Complete.
London Mathematical Society lecture note series ; 342. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b3844527x*spi |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Preface; Charles Thomas, 1938-2005; 1. Discrete torsion for the supersingular orbifold sigma genus; 1. Introduction; 2. The sigma orientation and the sigma genus; 3. The sigma genus; 4. The Borel-equivariant sigma genus; 5. Character theory; 6. The orbifold sigma genus; 7. Comparison with the analytic equivariant genus; 8. The cocycle; 9. Discrete torsion; 10. The non-abelian Case; References; 2. Quaternionic elliptic objects and K3-cohomology; 1. Introduction; 2. The sigma orientation and the sigma genus; 3. The sigma genus.
- 4. The Borel-equivariant sigma genus5. Character theory; 6. The orbifold sigma genus; 7. Comparison with the analytic equivariant genus; 8. The cocycle; 9. Discrete torsion; 10. The non-abelian Case; References; 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 <U+004b>X(Č)9. <U+005a> as a cubic refinement, with applications to integration over flat C-fields; 10. 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.8. Rational equivariant cohomology theories.; 9. The model for the circle group G = T.; 10. Reflecting the group structure of the elliptic curve.; References; 5. Delocalised equivariant elliptic cohomology (with an introduction by Matthew Ando and Haynes Miller); References; 6. On finite resolutions of K(n)-local spheres; 0. Introduction; 1. Background; 1.1 Localization with respect to Morava K-theory.; 1.2 The stabilizer groups.; 1.3 Homotopy xed point spectra.; 2. The case n= 0 mod p-1; 2.1 Explicit examples I; 2.2 The general case.
