Global Calculus

Global Calculus

by S. Ramanan
     
 

ISBN-10: 0821837028

ISBN-13: 9780821837023

Pub. Date: 12/07/2004

Publisher: American Mathematical Society

The power that analysis, topology and algebra bring to geometry has revolutionised 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

…  See more details below

Overview

The power that analysis, topology and algebra bring to geometry has revolutionised 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.

Read More

Product Details

ISBN-13:
9780821837023
Publisher:
American Mathematical Society
Publication date:
12/07/2004
Series:
Graduate Studies in Mathematics Series, #65
Pages:
316
Product dimensions:
7.20(w) x 10.20(h) x 0.90(d)

Table of Contents

Ch. 1Sheaves and differential manifolds : definitions and examples1
Ch. 2Differential operators27
Ch. 3Integration on differential manifolds73
Ch. 4Cohomology of sheaves and applications93
Ch. 5Connections on principal and vector bundles; lifting of symbols125
Ch. 6Linear connections171
Ch. 7Manifolds with additional structures185
Ch. 8Local analysis of elliptic operators229
Ch. 9Vanishing theorems and applications257
App. 1Algebra301
App. 2Topology305
App. 3Analysis307

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >