Year: 2006
Type: preprint
Abstract: We generalize the notion of graph minors to all (finite) simplicial complexes. For every two simplicial complexes H and K and every nonnegative integer m, we prove that if H is a minor of K then the non vanishing of Van Kampen's obstruction in dimension m (a characteristic class indicating non embeddability in the (m-1)-sphere) for H implies its non vanishing for K. As a corollary, based on results by Van Kampen and Flores, if K has the d-skeleton of the (2d+2)-simplex as a minor, then K is not embeddable in the 2d-sphere. We answer affirmatively a problem asked by Dey et. al. concerning topology-preserving edge contractions, and conclude from it the validity of the generalized lower bound inequalities for a special class of triangulated spheres.
Source: arXiv (Cornell University)
Author: Nevo, Eran
Institution: Hebrew University of Jerusalem
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949623196