Elliptic Operators, Topology, and Asymptotic Methods
Regular price
€248.00
14 days return policy
Shipping & Delivery
A01=John Roe
advanced index theorem applications
algebra
Author_John Roe
bundle
Category=PBKJ
clifford
Clifford Algebra
De Rham Cohomology
De Rham Complex
differential topology
dirac
Dirac Operator
eigenvalue analysis
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exterior Product
Functional Calculus
Galois Coverings
Garding Inequality
heat
Hilbert Schmidt Operator
Hodge decomposition
Holomorphic Function
index
Index Theorem
Kahler Manifold
kernel
Levi Civita Connection
Lie Algebra
manifold
Morse inequalities
partial differential equations
Ricci Curvature
riemannian
Riemannian Manifold
Smooth Sections
Smoothing Kernel
Smoothing Operator
spectral theory
Spin Bundle
Spin Manifold
Spin Representation
Tangent Bundle
Trace Class Operator
vector
Vector Bundle
Product details
- ISBN 9781138417670
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 15 Aug 2017
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem.
The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings.
The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.
