Algebraic shifting and basic constructions on simplicial complexes

Eran Nevo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We try to understand the behavior of algebraic shifting with respect to some basic constructions on simplicial complexes, such as union, coning, and (more generally) join. In particular, for the disjoint union of simplicial complexes we prove Δ(K ∪ L) = Δ(Δ(K) ∪ Δ(L)) (conjectured by Kalai [6]), and for the join we give an example of simplicial complexes K and L for which Δ(K*L) ≠ Δ(Δ(K) *Δ(L)) (disproving a conjecture by Kalai [6]), where Δ denotes the (exterior) algebraic shifting operator. We develop a 'homological' point of view on algebraic shifting which is used throughout this work.

Original languageAmerican English
Pages (from-to)411-433
Number of pages23
JournalJournal of Algebraic Combinatorics
Volume22
Issue number4
DOIs
StatePublished - Dec 2005

Keywords

  • Algebraic shifting
  • Simplicial complexes

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