Invariance Theory
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Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem(Studies in Advanced Mathematics)

Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem(Studies in Advanced Mathematics)


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About the Book

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.

Table of Contents:
Pseudo-Differential Operators Introduction Fourier Transform and Sobolev Spaces Pseudo-Differential Operators on Rm Pseudo-Differential Operators on Manifolds Index of Fredholm Operators Elliptic Complexes Spectral Theory The Heat Equation Local Index Formula Variational Formulas Lefschetz Fixed Point Theorems The Zeta Function The Eta Function Characteristic Classes Introduction Characteristic Classes of Complex Bundles Characteristic Classes of Real Bundles Complex Projective Space Invariance Theory The Gauss-Bonnet Theorem Invariance Theory and Pontrjagin Classes Gauss-Bonnet for Manifolds with Boundary Boundary Characteristic Classes Singer's Question The Index Theorem Introduction Clifford Modules Hirzebruch Signature Formula Spinors The Spin Complex The Riemann-Roch Theorem K-Theory The Atiyah-Singer Index Theorem The Regularity at s = 0 of the Eta Function Lefschetz Fixed Point Formulas Index Theorem for Manifolds with Boundary The Eta Invariant of Locally Flat Bundles Spectral Geometry Introduction Operators of Laplace Type Isospectral Manifolds Non-Minimal Operators Operators of Dirac Type Manifolds with Boundary Other Asymptotic Formulas The Eta Invariant of Spherical Space Forms A Guide to the Literature Acknowledgment Introduction Bibliography Notation

About the Author :
Gilkey, Peter B.


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Product Details
  • ISBN-13: 9780429600142
  • Publisher: Taylor & Francis Ltd
  • Publisher Imprint: CRC Press
  • Language: English
  • Sub Title: The Heat Equation and the Atiyah-Singer Index Theorem
  • ISBN-10: 0429600143
  • Publisher Date: 02 May 2018
  • Binding: Digital (delivered electronically)
  • Series Title: Studies in Advanced Mathematics


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Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem(Studies in Advanced Mathematics)
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Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem(Studies in Advanced Mathematics)
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