The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and pointset topology.The book's guiding philosophy is, in the words of Newton, that "in learning the sciences examples are of more use than precepts". We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a "global and analytical bias". We develop many algebraictopological techniques in the special context of smooth manifolds such as Poincare duality, Thom isomorphism, intersection theory, characteristic classes and the GaussBonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic "L"pand Holder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an indepth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.Contents: ManifoldsNatural Constructions on ManifoldsCalculus on ManifoldsRiemannian GeometryElements of the Calculus of VariationsThe Fundamental Group and Covering SpacesCohomologyCharacteristic ClassesClassical Integral Geometry Elliptic Equations on ManifoldsDirac OperatorsReadership: Mathematicians.
About Liviu I Nicolaescu
Regrettably, right now we simply cannot offer you info on the Publisher Liviu I Nicolaescu. However this does not always mean that individuals are unsuccessful for my child assortment. We all question which you assist us with this subject. For those who have free time and need will exceptionally appreciate in the event you give us the information you have. As soon as getting these kinds of opinions and knowledge by users about the Lectures on the Geometry of Manifolds Founder Liviu I Nicolaescu, many of us 1st the woman look at. Once many of us make certain that all correct, only post it. We all see why support as well as thanks in advance.Details Book
Author  :  Liviu I Nicolaescu 
Publisher  :  World Scientific Publishing Company 
Data Published  :  01 January 2007 
ISBN  :  128191150X 
EAN  :  9781281911506 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  589 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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