Accession Number : AD0690581

Title :   THE LOWER BOUND CONJECTURE FOR 3- AND 4-MANIFOLDS,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Walkup,David W.

Report Date : MAY 1969

Pagination or Media Count : 58

Abstract : The so-called lower bound conjecture for simplicial polytopes asserts that e(P) = or > d.v(P) - d(d+1)/2, where e(P) and v(P) denote respectively the number of edges and vertices of any simplicial d-polytope P, i.e., any closed bounded convex polyhedron of dimension d, all of whose faces are simplices. This paper establishes analogous lower bounds for arbitrary triangulations of closed topological 3- and 4-manifolds, including sharp lower bounds for the 3-sphere, the 3-dimensional analogues of the torus and Klein bottle, projective 3-space, and the 4-sphere with any number of handles. The results for the 3-sphere and 4-sphere immediately imply the previously unproven lower bound conjecture for simplicial 4- and 5-polytopes. The result for projective 3-space has similar implications for centrally symmetric simplicial 4-polytopes. (Author)

Descriptors :   (*TOPOLOGY, COMBINATORIAL ANALYSIS), GRAPHICS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE