Lectures On The Geometry Of Manifolds (2Nd Edition) - Softcover

Nicolaescu, Liviu I

Softcover

ISBN 10: 9812778624 ISBN 13: 9789812778628

Publisher: Wspc, 2007

Synopsis

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 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 Poincaré 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 Hölder 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.

About this title

Review

... advanced graduate students will find the present book a fine text and reference. Virtually everything is created from scratch and presented in a thoughtful manner ... the chapter on cohomology is really a tour-de-force, involving geometry, topology and analysis in a fashion that every graduate student should see ... All-in-all, this is an excellent book for the right audience ... this book has everything for a full year-long course introducing students to the modern workings of global analysis. --Zentralblatt MATH

Edition details

• Publisher: Wspc
• Publication date: 2007
• ISBN 10: 9812778624
• ISBN 13: 9789812778628
• Binding: Paperback
• Language: English
• Edition number: 2
• Number of pages: 608