Boek
This book is an introduction to manifolds at the beginning graduate level. Itcontains the essential topological ideas that are needed for the further studyof manifolds particularly in the context of differential geometry algebraictopology and related fields. Its guiding philosophy is to develop these ideasrigorously but economically with minimal prerequisites and plenty of geometricintuition. A course on manifolds differs from most other introductorymathematics graduate courses in that the subject matter is often completelyunfamiliar. Unlike algebra and analysis which all math majors see asundergraduates manifolds enter the curriculum much later. It is even possibleto get through an entire undergraduate mathematics education without everhearing the word quotmanifold.quot Yet manifolds are part of the basicvocabulary of modern mathematics and students need to know them as intimatelyas they know the integers the real numbers Euclidean spaces groups ringsand fields. In his beautifully conceived introduction the author motivates thetechnical developments to follow by explaining some of the roles manifolds playin diverse branches of mathematics and physics. Then he goes on to introducethe basics of general topology and continues with the fundamental groupcovering spaces and elementary homology theory. Manifolds are introduced earlyand used as the main examples throughout. John M. Lee is currently Professor ofMathematics at the University of Washington. TOCIntroduction. GeneralTopology. New Spaces From Old. Compactness and Connectedness. Surfaces.Homotopy and the Fundamental Group. The Circle. Some Group Theory.Fundamental Groups of Surfaces. Covering Spaces. Classification of CoveringSpaces. «
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