Algebraic Shifting and Basic Constructions on Simplicial Complexes
| dc.creator | Nevo, Eran | |
| dc.date | 2003-03-19 | |
| dc.date | 2006-02-23 | |
| dc.date.accessioned | 2026-07-07T06:35:36Z | |
| dc.date.available | 2026-07-07T06:35:36Z | |
| dc.description | We try to understand the behavior of exterior algebraic shifting with respect to basic constructions on simplicial complexes, like union and join. In particular we give a complete combinatorial description of the shifting of a disjoint union, and more generally of a union along a simplex, in terms of the shifting of its components. As a corollary, we prove the following, conjectured by Kalai: $Δ(K \cup L) = Δ(Δ(K) \cup Δ(L))$, where $K,L$ are complexes, $\cup$ means disjoint union, and $Δ$ is the exterior shifting operator. We give an example showing that replacing the operation 'union' with the operation 'join' in the above equation is wrong, disproving a conjecture made by Kalai. We adopt a homological point of view on the algebraic shifting operator, which is used throughout this work. | |
| dc.description | Final version: 24 pages, no figures. Proof of Proposition 4.5 improved, minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0303233 | |
| dc.identifier | http://arxiv.org/abs/math/0303233 | |
| dc.identifier | J. Algeb. Combi., 22 (2005), 411-433 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99843 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | 05E99; 13D99; 13F55 | |
| dc.title | Algebraic Shifting and Basic Constructions on Simplicial Complexes | |
| dc.type | text |