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Algebraic Topology via Differential Geometry (London Mathematical Society Lecture Note Series)
Rok: 1988
ISBN: 9780521317146
OKCZID: 110111285
Citace (dle ČSN ISO 690):
KAROUBI, Max. Algebraic topology via differential geometry. 1st pub. Cambridge: Cambridge University Press, 1989. 363 s. London Mathematical Society lecture note series, 99.
Anotace
In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.