de Rham-Sullivan Measure of Spaces and Its Calculability

Wu Wen-tsün
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Wu Wen-tsün: Academia Sinica, Institute of Systems-Science

A chapter in The Chern Symposium 1979, 1980, pp 229-245 from Springer

Abstract: Abstract In the first paper on L’Analysis Situs, dated 1895, Poincaré introduced fundamental notions which are nowadays called differential manifolds, complexes, Betti numbers, fundamental groups, etc., thus laying down the foundations of modern algebraic topology. In addition Poincaré posed the problem of determining the Betti numbers of differential manifolds by means of exterior differential forms; see Section 9 of that paper. The problem was clarified by E. Cartan, and only in 1931 was it completely solved by de Rham. The result, now known as the de Rham theorem, may be stated as follows.

Keywords: Spectral Sequence; Betti Number; Algebraic Topology; Riemannian Symmetric Space; Finite Complex (search for similar items in EconPapers)
Date: 1980
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DOI: 10.1007/978-1-4613-8109-9_10

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