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