WS 21
Seminar Topology
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Topic ELLIPTIC GENERA OF SMOOTH MANIFOLDS.
Registration per MÜSLI.
| Date: | Topics: | Status: |
|---|---|---|
| 21.4.22 | Introduction | Reserved |
| 28.4.22 | 1.1, 1.2, 1.3, 1.4 (Cobordism, char. classes) | Reserved |
| 5.5.22 | 1.5, 1.6, 1.7 (Representations, mult. sequences, genera) | Reserved |
| 12.5.22 | 1.8, 2.1, 2.2 (Complex and elliptic genera) | Reserved |
| 19.5.22 | 3.1, 3.2, 4.1 (Virtual submanifolds, universal genus, signature and L-genus) | Reserved |
| 2.6.22 | 4.2, 4.3, 4.4 (vertical tangent bundle, multiplicativity in fiber bundles, splitting principle) | Reserved |
| 9.6.22 | 4.5, 4.6, 5.1 (integration along the fiber, multiplicativity, elliptic operators) | Reserved |
| 23.6.22 | 5.2, 5.3, 5.4, 5.5 (Atiyah-Singer index theorem, de Rham and Dolbeault complex, signature as index) | Reserved |
| 30.6.22 | 5.6, 5.7, 5.8 (Equivariant index, circle actions) | Reserved |
| 7.7.22 | Appendix I.1, 6.1 augmented by material from App. I (Modular form theory, elliptic genera after Witten) | Reserved |
| 21.7.22 | 6.2, 6.3 (Expansion at cusp 0, twisted A^-genus, Witten genus) | Reserved |
| 28.7.22 | 6.3, 6.4, (6.5 time permitting) (Witten genus and the Lie group E_8) | Available |
Literature: F. Hirzebruch, T. Berger, R. Jung, Manifolds and Modular Forms, 2nd edition, Aspects of Math., Max Planck Institut für Mathematik Bonn, Springer Fachmedien Wiesbaden 1994.