000			02161cam a22002414a 4500
008			000225s2011 nyua b 001 0 eng
020			_a9781441979391
082	0	0	_a514.3 _bLEE
100	1		_aLee, John M.
245	1	0	_aIntroduction to topological manifolds
250			_a2nd ed.
260			_aNew York: _bSpringer, _c2011
300			_a385 p.: _bill.; _c24 cm
365			_aINR _b4600.56
440		0	_aGraduate texts in mathematics: Vol. 202
504			_aIncludes bibliographical references and index.
520			_a This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the word "manifold." Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields. In his beautifully conceived introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics. Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout. John M. Lee is currently Professor of Mathematics at the University of Washington
650		0	_aTopological space
650		0	_aVan Kampen Theorem
650		0	_aHomology
650		0	_aSeifert
942			_2ddc _cTD
999			_c44512 _d44512