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dc.contributor.authorJojic, Dusko
dc.contributor.authorNekrasov, Ilya
dc.contributor.authorPanina, Gaiane
dc.contributor.authorZivaljevic, Rade
dc.date.accessioned2016-10-25T12:29:23Z
dc.date.available2016-10-25T12:29:23Z
dc.date.issued2016-10
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1255
dc.descriptionResearch in Pairs 2016en_US
dc.description.abstractWe introduce and study Alexander $r$-Tuples $\mathcal{K} = \langle K_i \rangle ^r_{i=1}$ of simplicial complexes, as a common generalization of pairs of Alexander dual complexes (Alexander 2-tuples) and r-unavoidable complexes of [BFZ-1]. In the same vein, the Bier complexes, defined as the deleted joins $\mathcal{K}^*_\Delta$ of Alexander $r$-tuples, include both standard Bier spheres and optimal multiple chessboard complexes (Section 2.2) as interesting, special cases. Our main results are Theorem 4.3 saying that (1) the $r$-fold deleted join of Alexander $r$-tuple is a pure complex homotopy equivalent to a wedge of spheres, and (2) the $r$-fold deleted join of a collective unavoidable $r$-tuple is $(n - r - 1)$-connected, and a classification theorem (Theorem 5.1 and Corollary 5.2) for Alexander $r$-tuples and Bier complexes.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2016,17
dc.subjectBier spheresen_US
dc.subjectAlexander dualityen_US
dc.subjectChessboard complexesen_US
dc.subjectUnavoidable complexesen_US
dc.subjectDiscrete Morse theoryen_US
dc.titleAlexander r-Tuples and Bier Complexesen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2016-17
local.scientificprogramResearch in Pairs 2016en_US
local.series.idOWP-2016-17
dc.identifier.urnurn:nbn:de:101:1-20161010260
dc.identifier.ppn1658987578


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