The object of this book is to introduce the reader to some of the most important techniques of modern global geometry. It mainly deals with global questions and in particular the interdependence of geometry and topology, global and local. Algebraicotopological techniques are developed in the special context of smooth manifolds. The book discusses the DeRham cohomology and its ramifications: Poincare, duality, intersection theory, degree theory, Thom isomorphism, characteristic classes, GaussBonnet etc. The authors seek to calculate the cohomology groups of as many as possible concrete examples without relying on the apparatus of homotopy theory (CWcomplexes etc). Elliptic partial differential equations are also featured, requiring a familiarity with functional analysis. It describes the proofs of elliptic Lp and Holder estimates (assuming some deep results of harmonic analysis) for arbitrary elliptic operators with smooth coefficients. The book closes with alook at a class of elliptic operators, the Dirac operators. It discusses their algebraic structure in some detail, Weizenbock formulae and many concrete examples.
About Liviu I. Nicolaescu
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Author  :  Liviu I. Nicolaescu 
Publisher  :  World Scientific Publishing Co Pte Ltd 
Data Published  :  12 January 1996 
ISBN  :  9810228368 
EAN  :  9789810228361 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  500 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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