**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

**Introduction to Mathematical Physics**

by

**Alex Madon**-

**Wikibooks**

The goal of this book is to propose an ensemble view of modern physics. The coherence between various fields of physics is insured by following two axes: a first is the universal mathematical language; the second is the study of the N body problem.

(

**3562**views)

**Mathemathical Methods of Theoretical Physics**

by

**Karl Svozil**-

**Edition Funzl**

This book presents the course material for mathemathical methods of theoretical physics intended for an undergraduate audience. The author most humbly presents his own version of what is important for standard courses of contemporary physics.

(

**4617**views)

**An Introduction to Hyperbolic Analysis**

by

**Andrei Khrennikov, Gavriel Segre**-

**arXiv**

Contents: The hyperbolic algebra as a bidimensional Clifford algebra; Limits and series in the hyperbolic plane; The hyperbolic Euler formula; Analytic functions in the hyperbolic plane; Multivalued functions on the hyperbolic plane; etc.

(

**7031**views)

**A Set of Appendices on Mathematical Methods for Physics Students**

by

**Anne Fry, Amy Plofker, Sarah-marie Belcastro**

Useful mathematical background for physics students at all undergraduate levels. Topics: Matrices, Eigenvalues and Eigenvectors, Intro To Differential Equations, Integration, Fourier Analysis and Transforms, Converting Sums to Integrals, etc.

(

**5267**views)