Accession Number : AD0427407


Title :   COBORDISM AND THE EULER NUMBER,


Corporate Author : MARTIN MARIETTA CORP BALTIMORE MD RESEARCH INST FOR ADVANCED STUDIES


Personal Author(s) : Reinhart, Bruce L


Report Date : 15 May 1963


Pagination or Media Count : 5


Abstract : The Euler number is obtained as a cobordism invariant by making a more stringent definition of cobordism, requiring the existence of a nonsingular vector field interior normal on one of a pair of cobording manifolds and exterior normal on the other. The new cobordism groups admit natural homorphisms into the usual ones having as kernels cyclic groups generated by spheres. In even dimensions, these kernels are free cyclic and give the Euler number as an additional invariant. In odd dimensions, the kernels are zero except in oriented cobordism of dimension 4k + 1, where the kernel is cyclic of order 2. In this case, two manifolds are cobordant if and only if they have the same Stiefel-Whitney numbers and bound a manifold of even Euler number. In the oriented case, the kernel is a direct summand, while in the nonoriented case, the even dimensional real projective spaces become of infinite order. (Author)


Descriptors :   *ALGEBRAIC TOPOLOGY , RELATIVITY THEORY , TOPOLOGY , GROUPS(MATHEMATICS) , DIFFERENTIAL EQUATIONS , RINGS


Distribution Statement : APPROVED FOR PUBLIC RELEASE