TY - JOUR
T1 - Algebraic shifting and basic constructions on simplicial complexes
AU - Nevo, Eran
PY - 2005/12
Y1 - 2005/12
N2 - 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.
AB - 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.
KW - Algebraic shifting
KW - Simplicial complexes
UR - http://www.scopus.com/inward/record.url?scp=33144486495&partnerID=8YFLogxK
U2 - 10.1007/s10801-005-4626-0
DO - 10.1007/s10801-005-4626-0
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AN - SCOPUS:33144486495
SN - 0925-9899
VL - 22
SP - 411
EP - 433
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 4
ER -