Nankai Tracts in Mathematics - Vol. 2
THE INDEX THEOREM AND THE HEAT EQUATION METHOD
by Y L Yu (Suzhou University, China)
This book provides a self-contained representation of the local version of the Atiyah–Singer index theorem. It contains proofs of the Hodge theorem, the local index theorems for the Dirac operator and some first order geometric elliptic operators by using the heat equation method. The proofs are up to the standard of pure mathematics. In addition, a Chern root algorithm is introduced for proving the local index theorems, and it seems to be as efficient as other methods.
Contents:
- Preliminaries in Riemannian Geometry
- Schrödinger and Heat
Operators
- MP Parametrix and Applications
- Chern–Weil Theory
- Clifford Algebra and Super-Algebra
- Dirac Operator
- Local Index Theorems
- Riemann–Roch Theorem
Readership: Researchers and graduate students in mathematics.
"The book is self-contained, which is most helpful for graduate students."
| Mathematical Reviews, 2002 |
"This is a lovely book on the local version of the Atiyah-Singer index theorem and the heat equation method ... it is reasonably self-contained and could serve as the starting point for studies of the index theorem."
| Mathematics Abstracts, 2002 |
| 308pp |
Pub. date: Jul 2001 |
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