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
Topics in Spectral Theoryby Vojkan Jaksic - McGill University
The subject of these lecture notes is spectral theory of self-adjoint operators and some of its applications to mathematical physics. The main theme is the interplay between spectral theory of self-adjoint operators and classical harmonic analysis.
(5596 views)
Little Magnetic Bookby Nicolas Raymond - arXiv
'Little Magnetic Book' is devoted to the spectral analysis of the magnetic Laplacian in various geometric situations. In particular the influence of the geometry on the discrete spectrum is analysed in many asymptotic regimes.
(2976 views)
Clifford Algebra, Geometric Algebra, and Applicationsby Douglas Lundholm, Lars Svensson - arXiv
These are lecture notes for a course on the theory of Clifford algebras. The various applications include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.
(9918 views)
Mathematical Physics IIby Boris Dubrovin - SISSA
These are lecture notes on various topics in analytic theory of differential equations: Singular points of solutions to analytic differential equations; Monodromy of linear differential operators with rational coefficients.
(11908 views)