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Lectures on the Geometry of Manifolds by Liviu I. Nicolaescu (2007, Trade Paperback)

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About this product

Product Identifiers

PublisherWorld Industries Scientific Publishing Co Pte LTD

ISBN-109812778624

ISBN-139789812778628

eBay Product ID (ePID)63453135

Product Key Features

Number of Pages589 Pages

LanguageEnglish

Publication NameLectures on the Geometry of Manifolds

Publication Year2007

SubjectGeometry / Differential, Geometry / Algebraic

TypeTextbook

Subject AreaMathematics

AuthorLiviu I. Nicolaescu

FormatTrade Paperback

Dimensions

Item Height1.2 in

Item Weight0 Oz

Item Length9.7 in

Item Width6.6 in

Additional Product Features

Edition Number2

Intended AudienceTrade

Dewey Edition20

IllustratedYes

Dewey Decimal780

SynopsisThe 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 point-set 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 algebraic-topological techniques in the special context of smooth manifolds such as Poincar duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-Bonnet 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 Lpand H lder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth 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.