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de Rham-Sullivan Measure of Spaces and Its Calculability

In: The Chern Symposium 1979

Author

Listed:
  • Wu Wen-tsün

    (Academia Sinica, Institute of Systems-Science)

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.

Suggested Citation

  • Wu Wen-tsün, 1980. "de Rham-Sullivan Measure of Spaces and Its Calculability," Springer Books, in: W.-Y. Hsiang & S. Kobayashi & I. M. Singer & J. Wolf & H.-H. Wu & A. Weinstein (ed.), The Chern Symposium 1979, pages 229-245, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-8109-9_10
    DOI: 10.1007/978-1-4613-8109-9_10
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