Invariance Theory, the Heat Equation and the Atiyah-Singer Index Theorem
by Peter B. Gilkey
Publisher: Publish or Perish Inc. 1984
ISBN/ASIN: 0849378745
Number of pages: 536
Description:
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.
Download or read it online for free here:
Download link
(DVI, PS)
Similar books
Mirror Symmetryby Cumrun Vafa, Eric Zaslow - American Mathematical Society
The book provides an introduction to the field of mirror symmetry from both a mathematical and physical perspective. After covering the relevant background material, the monograph is devoted to the proof of mirror symmetry from various viewpoints.
(11718 views)
Differential Equations of Mathematical Physicsby Max Lein - arXiv
These lecture notes give an overview of how to view and solve differential equations that are common in physics. They cover Hamilton's equations, variations of the Schroedinger equation, the heat equation, the wave equation and Maxwell's equations.
(7725 views)
Three Lectures on Complexity and Black Holesby Leonard Susskind - arXiv.org
The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes...
(3333 views)
Mathematics for Theoretical Physicsby Jean Claude Dutailly - arXiv
This is a comprehensive and precise coverage of the mathematical concepts and tools used in present theoretical physics: differential geometry, Lie groups, fiber bundles, Clifford algebra, differential operators, normed algebras, connections, etc.
(12536 views)