This book provides a comprehensive introduction to the theory of elliptic genera due to Ochanine, Landweber, Stong, and others. The theory describes a new cobordism invariant for manifolds in terms of modular forms. The book evolved from notes of a course given at the University of Bonn. After providing some background material elliptic genera are constructed, including the classical genera signature and the index of the Dirac operator as special cases. Various properties of elliptic genera are discussed, especially their behaviour in fibre bundles and rigidity for group actions. For stably almost complex manifolds the theory is extended to elliptic genera of higher level. The text is in most parts self-contained. The results are illustrated by explicit examples and by comparison with well-known theorems. The relevant aspects of the theory of modular forms are derived in a seperate appendix, providing also a useful reference for mathematicians working in this field.
- ISBN10 352816414X
- ISBN13 9783528164140
- Publish Date 1 January 1994
- Publish Status Active
- Out of Print 26 December 2011
- Publish Country DE
- Publisher Springer Fachmedien Wiesbaden
- Imprint Vieweg+Teubner Verlag
- Edition 2nded. 1994
- Format Paperback
- Pages 212
- Language English