
Accession Number : AD0690581
Title : THE LOWER BOUND CONJECTURE FOR 3 AND 4MANIFOLDS,
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 socalled 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 dpolytope 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 4manifolds, including sharp lower bounds for the 3sphere, the 3dimensional analogues of the torus and Klein bottle, projective 3space, and the 4sphere with any number of handles. The results for the 3sphere and 4sphere immediately imply the previously unproven lower bound conjecture for simplicial 4 and 5polytopes. The result for projective 3space has similar implications for centrally symmetric simplicial 4polytopes. (Author)
Descriptors : (*TOPOLOGY, COMBINATORIAL ANALYSIS), GRAPHICS, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE