Invariance Theory
Title | Invariance Theory PDF eBook |
Author | Peter B. Gilkey |
Publisher | CRC Press |
Pages | 534 |
Release | 1994-12-22 |
Genre | Mathematics |
ISBN | 9780849378744 |
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.
The Index Theorem And The Heat Equation Method
Title | The Index Theorem And The Heat Equation Method PDF eBook |
Author | Yanlin Yu |
Publisher | World Scientific |
Pages | 309 |
Release | 2001-07-02 |
Genre | Science |
ISBN | 981449111X |
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.
Heat Kernels and Dirac Operators
Title | Heat Kernels and Dirac Operators PDF eBook |
Author | Nicole Berline |
Publisher | Springer Science & Business Media |
Pages | 384 |
Release | 2003-12-08 |
Genre | Mathematics |
ISBN | 9783540200628 |
In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback.
The Index Theorem and the Heat Equation
Title | The Index Theorem and the Heat Equation PDF eBook |
Author | Peter B. Gilkey |
Publisher | Publish or Perish |
Pages | 134 |
Release | 1974 |
Genre | Mathematics |
ISBN |
The Atiyah-Patodi-Singer Index Theorem
Title | The Atiyah-Patodi-Singer Index Theorem PDF eBook |
Author | Richard Melrose |
Publisher | CRC Press |
Pages | 392 |
Release | 1993-03-31 |
Genre | Mathematics |
ISBN | 1439864608 |
Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
The Laplacian on a Riemannian Manifold
Title | The Laplacian on a Riemannian Manifold PDF eBook |
Author | Steven Rosenberg |
Publisher | Cambridge University Press |
Pages | 190 |
Release | 1997-01-09 |
Genre | Mathematics |
ISBN | 9780521468312 |
This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Elliptic Operators, Topology, and Asymptotic Methods
Title | Elliptic Operators, Topology, and Asymptotic Methods PDF eBook |
Author | John Roe |
Publisher | Longman Scientific and Technical |
Pages | 208 |
Release | 1988 |
Genre | Mathematics |
ISBN |