Annali di Matematica Pura ed Applicata

, Volume 98, Issue 1, pp 1–24 | Cite as

Cup-product e prodotto esterno

  • Enzo Martinelli


Alternating cup-product for alternating singular cochains and cohomology classes, over a field of characteristic zero, is considered. Differently from ordinary cup-product, the alternating one is skew-commutative for cochains also, and exactly parallel to exterior product for differential forms. A direct proof of de Rham's third theorem follows, with use of a convenient simplicial (but not barycentric) subdivision.


  1. [1]
    M. J. Greenberg,Lectures on Algebraic Topology, Benjamin Inc., New York (1967).Google Scholar
  2. [2]
    P. J. Hilton-S. Wylie,Homology Theory, Cambridge University Press (1960).Google Scholar
  3. [3]
    E. Martinelli,Omologia e coomologia singolari, orientata e alternante, Rend. Acc. Naz. Lincei,53 (1972), pp. 264–274.MathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1974

Authors and Affiliations

  • Enzo Martinelli
    • 1
  1. 1.Roma

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