Accession Number : AD0648983

Title :   THE COHOMOLOGY RING OF A SMOOTH MANIFOLD.

Descriptive Note : Technical rept.,

Corporate Author : WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS

Personal Author(s) : Carrell,James B.

Report Date : MAR 1967

Pagination or Media Count : 50

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)

Descriptors :   (*ALGEBRAIC TOPOLOGY, ALGEBRA), DIFFERENTIAL GEOMETRY, THEORY, GROUPS(MATHEMATICS)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE