Higher minors and Van Kampen's obstruction

Eran Nevo

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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 [19] and Flores [4], 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. [2] concerning topology-preserving edge contractions, and conclude from it the validity of the generalized lower bound inequalities for a special class of triangulated spheres.

Original languageEnglish
Pages (from-to)161-176
Number of pages16
JournalMathematica Scandinavica
Volume101
Issue number2
DOIs
StatePublished - 1 Jan 2007
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

Fingerprint

Dive into the research topics of 'Higher minors and Van Kampen's obstruction'. Together they form a unique fingerprint.

Cite this