Squeezed complexes

DC FieldValueLanguage
dc.contributor.authorJuhnke-Kubitzke, Martina
dc.contributor.authorNagel, Uwe
dc.date.accessioned2021-12-23T16:07:36Z-
dc.date.available2021-12-23T16:07:36Z-
dc.date.issued2020
dc.identifier.issn00246107
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/7956-
dc.description.abstractGiven a shifted order ideal U, we associate to it a family of simplicial complexes (Delta t(U))t > 0 that we call squeezed complexes. In a special case, our construction gives squeezed balls that were defined and used by Kalai to show that there are many more simplicial spheres than boundaries of simplicial polytopes. We study combinatorial and algebraic properties of squeezed complexes. In particular, we show that they are vertex decomposable and characterize when they have the weak or the strong Lefschetz property. Moreover, we define a new combinatorial invariant of pure simplicial complexes, called the singularity index, that can be interpreted as a measure of how far a given simplicial complex is from being a manifold. In the case of squeezed complexes (Delta t(U))t > 0, the singularity index turns out to be strictly decreasing until it reaches (and stays) zero if t grows.
dc.description.sponsorshipGerman Research CouncilGerman Research Foundation (DFG) [DFG GRK-1916]; Simons Foundation [317096]; The first author was supported by the German Research Council DFG GRK-1916. The second author was partially supported by Simons Foundation grant #317096.
dc.language.isoen
dc.publisherWILEY
dc.relation.ispartofJOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
dc.subject05E40
dc.subject13F55 (primary)
dc.subjectIDEALS
dc.subjectLEFSCHETZ PROPERTY
dc.subjectMathematics
dc.subjectWEAK
dc.titleSqueezed complexes
dc.typejournal article
dc.identifier.doi10.1112/jlms.12261
dc.identifier.isiISI:000479566600001
dc.description.volume101
dc.description.issue1
dc.description.startpage110
dc.description.endpage135
dc.identifier.eissn14697750
dc.publisher.place111 RIVER ST, HOBOKEN 07030-5774, NJ USA
dcterms.isPartOf.abbreviationJ. Lond. Math. Soc.-Second Ser.
crisitem.author.deptFB 06 - Mathematik/Informatik-
crisitem.author.deptidfb06-
crisitem.author.parentorgUniversität Osnabrück-
crisitem.author.netidJuMa420-
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