Graduate Studies in Mathematics 2005; 316 pp; hardcover Volume: 65 ISBN10: 0821837028 ISBN13: 9780821837023 List Price: US$61 Member Price: US$48.80 Order Code: GSM/65
 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 selfcontained 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. Readership Graduate students and research mathematicians interested in differential or algebraic geometry. Table of Contents  Sheaves and differential manifolds: Definitions and examples
 Differential operators
 Integration on differential manifolds
 Cohomology of sheaves and applications
 Connections on principal and vector bundles; Lifting of symbols
 Linear connections
 Manifolds with additional structures
 Local analysis of elliptic operators
 Vanishing theorems and applications
 Appendix
 Bibliography
 Index
