Elliptic Operators, Topology, and Asymptotic Methods. (2017)
- Record Type:
- Book
- Title:
- Elliptic Operators, Topology, and Asymptotic Methods. (2017)
- Main Title:
- Elliptic Operators, Topology, and Asymptotic Methods
- Further Information:
- Note: John Roe.
- Authors:
- Roe, John
- Contents:
- Cover; Half Title; Title Page; Copyright Page; Dedication; Contents; Introduction; CHAPTER 1 Resumé of Riemannian geometry; Connections; Riemannian geometry; Differential forms; Exercises; CHAPTER 2 Connections, curvature, and characteristic classes; Principal bundles and their connections; Characteristic classes; Genera; Notes; Exercises; CHAPTER 3 Clifford algebras and Dirac operators; Clifford bundles and Dirac operators; Clifford bundles and curvature; Examples of Clifford bundles; Notes; Exercises; CHAPTER 4 The Spin groups; The Clifford algebra as a superalgebra Groups of invertibles in the Clifford algebraRepresentation theory of the Clifford algebra; Spin structures on manifolds; Spin bundles and characteristic classes; The complex Spin group; Notes; Exercises; CHAPTER 5 Analytic properties o f Dirac operators; Sobolev Spaces; Analysis of the Dirac operator; The functional calculus; Notes; Exercises; CHAPTER 6 Hodge theory; Notes; Exercises; CHAPTER 7 The heat and wave equations; Existence and uniqueness theorem s; The asymptotic expansion for the heat kernel; Finite propagation speed for the wave equation; Notes; Exercises CHAPTER 8 Traces and eigenvalue asymptoticsEigenvalue growth; Trace-class operators; Weyl's asymptotic formula; Notes; Exercises; CHAPTER 9 Some non-compact manifolds; The harmonic oscillator; Witten's perturbation of the de Rham complex; Functional calculus on open manifolds; Notes; Exercises; CHAPTER 10 The Lefschetz formula; Lefschetz numbers;Cover; Half Title; Title Page; Copyright Page; Dedication; Contents; Introduction; CHAPTER 1 Resumé of Riemannian geometry; Connections; Riemannian geometry; Differential forms; Exercises; CHAPTER 2 Connections, curvature, and characteristic classes; Principal bundles and their connections; Characteristic classes; Genera; Notes; Exercises; CHAPTER 3 Clifford algebras and Dirac operators; Clifford bundles and Dirac operators; Clifford bundles and curvature; Examples of Clifford bundles; Notes; Exercises; CHAPTER 4 The Spin groups; The Clifford algebra as a superalgebra Groups of invertibles in the Clifford algebraRepresentation theory of the Clifford algebra; Spin structures on manifolds; Spin bundles and characteristic classes; The complex Spin group; Notes; Exercises; CHAPTER 5 Analytic properties o f Dirac operators; Sobolev Spaces; Analysis of the Dirac operator; The functional calculus; Notes; Exercises; CHAPTER 6 Hodge theory; Notes; Exercises; CHAPTER 7 The heat and wave equations; Existence and uniqueness theorem s; The asymptotic expansion for the heat kernel; Finite propagation speed for the wave equation; Notes; Exercises CHAPTER 8 Traces and eigenvalue asymptoticsEigenvalue growth; Trace-class operators; Weyl's asymptotic formula; Notes; Exercises; CHAPTER 9 Some non-compact manifolds; The harmonic oscillator; Witten's perturbation of the de Rham complex; Functional calculus on open manifolds; Notes; Exercises; CHAPTER 10 The Lefschetz formula; Lefschetz numbers; The fixed-point contributions; Notes; Exercises; CHAPTER 11 The index problem; Gradings and Clifford bundles; Graded Dirac operators; The heat equation and the index theorem; Notes; Exercises Renormalized dimensions and the index theoremNotes; References; Index … (more)
- Edition:
- Second edition
- Publisher Details:
- Boca Raton, FL : CRC Press
- Publication Date:
- 2017
- Copyright Date:
- 1998
- Extent:
- 1 online resource
- Subjects:
- 515.3533
Elliptic operators
Index theorems
Global analysis (Mathematics)
Geometry, Differential
Differential equations
Geometry
Mathematical physics
Electronic books - Languages:
- English
- ISBNs:
- 9781482247831
1482247836
9780582325029 - Related ISBNs:
- 9781138417670
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.282817
- Ingest File:
- 01_189.xml