000			02200nam a22002777a 4500
003			IIITD
005			20240302174015.0
008			240223b xxu||||| |||| 00| 0 eng d
020			_a9781470437275
040			_aIIITD
082			_a514.7 _bGUI-D
100			_aGuillemin, Victor
245			_aDifferential topology _cby Victor Guillemin and Alan Pollack.
260			_aTelangana : _bAmerican Mathematical Society, _c©2010
300			_axvi, 222 p. _bill. ; _c23cm.
504			_aIncludes bibliographical references (212-215) and index.
505			_tPart-1 Manifolds and smooth Maps _tPart-2 Transversality and Intersection _tPart-3 Oriented intersection Theory _tPart-4 Integration on Manifolds
520			_aDifferential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea--transversality--the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincaré-Hopf index theorem, and Stokes theorem. The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance. The book is suitable for either an introductory graduate course or an advanced undergraduate course.
650			_a1. Differential topology
650			_aEvenness of zero
650			_aManifold
650			_aTransversality theorem
650			_aVictor Guillemin
700			_aPollack, Alan
942			_2ddc _cBK
999			_c172262 _d172262