**Graduate Studies in Mathematics**

Volume: 65;
2005;
316 pp;
Hardcover

MSC: Primary 14; 32; 53;

Print ISBN: 978-0-8218-3702-3

Product Code: GSM/65

List Price: $65.00

Individual Member Price: $52.00

**Electronic ISBN: 978-1-4704-2107-6
Product Code: GSM/65.E**

List Price: $65.00

Individual Member Price: $52.00

#### Supplemental Materials

# Global Calculus

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*S. Ramanan*

Analysis, topology and algebra brought new power to
geometry, revolutionizing the way geometers and physicists look at conceptual
problems. Some of the key ingredients in this interplay are sheaves,
cohomology, Lie groups, connections and differential operators. In
*Global Calculus*, the appropriate formalism for these topics is laid
out with numerous examples and applications by one of the experts in
differential and algebraic geometry.

Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book.

The book is suitable for a first year graduate course on global analysis.

#### Table of Contents

# Table of Contents

## Global Calculus

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface ix10 free
- Chapter 1. Sheaves and Differential Manifolds: Definitions and Examples 114 free
- Chapter 2. Differential Operators 2740
- Chapter 3. Integration on Differential Manifolds 7386
- Chapter 4. Cohomology of Sheaves and Applications 93106
- Chapter 5. Connections on Principal and Vector Bundles; Lifting of Symbols 125138
- Chapter 6. Linear Connections 171184
- Chapter 7. Manifolds with Additional Structures 185198
- 1. Reduction of the Structure Group 185198
- 2. Torsion Free G-Connections 194207
- 3. Complex Manifolds 197210
- 4. The Outer Gauge Group 201214
- 5. Riemannian Geometry 207220
- 6. Riemannian Curvature Tensor 211224
- 7. Ricci, Scalar and Weyl Curvature Tensors 219232
- 8. Clifford Structures and the Dirac Operator 224237

- Chapter 8. Local Analysis of Elliptic Operators 229242
- Chapter 9. Vanishing Theorems and Applications 257270
- Appendix 301314
- Bibliography 311324
- Index 313326
- Back Cover Back Cover1330

#### Readership

Graduate students and research mathematicians interested in differential or algebraic geometry.