THE COHOMOLOGY RING OF A SMOOTH MANIFOLD.
Abstract
C. B. Allendorfer and J. Eells, Jr. have used pairs of singular differential forms to describe a cohomology theory alpha *(X,A) for any smooth paracompact manifold. This theory strengthens the de Rham theory since the coefficient group A may be taken to be any subring of the reals. Their main result is that alpha *(X,A) is canonically isomorphic to the Cech cohomology module H(X,A) of X with coefficients in A. The purpose of this paper is to describe a natural cup product for alpha *(X,A) so that alpha *(X,A) becomes a ring canonically isomorphic with the Cech cohomology ring H(X,A). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1967
- Accession Number
- AD0648983
Entities
People
- James B. Carrell
Organizations
- University of Washington