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dc.contributor.authorŽivaljević, Radeen
dc.date.accessioned2020-04-12T18:03:56Z-
dc.date.available2020-04-12T18:03:56Z-
dc.date.issued2015-03-01en
dc.identifier.issn1230-3429en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/285-
dc.description.abstractWe compute a primary cohomological obstruction to the existence of an equipartition for j mass distributions in ℝd by two hyperplanes in the case 2d‒3j = 1. The central new result is that such an equipartition always exists if d = 6 · 2k + 2 and j = 4 · 2k + 1 which for k = 0 reduces to the main result of the paper P. Mani-Levitska et al., Topology and combinatorics of partitions of masses by hyperplanes, Adv. Math. 207 (2006), 266‒296. The theorem follows from a Borsuk‒Ulam type result claiming the non-existence of a D8-equivariant map f : Sd × Sd ® S(W⊕j) for an associated real D8-module W. This is an example of a genuine combinatorial geometric result which involves ℤ/4-torsion in an essential way and cannot be obtained by the application of either Stiefel‒Whitney classes or cohomological index theories with ℤ/2 or Z coefficients. The method opens a possibility of developing an “effective primary obstruction theory” based on G-manifold complexes, with applications in geometric combinatorics, discrete and computational geometry, and computational algebraic topology.en
dc.publisherJuliusz Schauder Center for Nonlinear Analysis-
dc.relation.ispartofTopological Methods in Nonlinear Analysisen
dc.subjectComputational topology | Equipartitions of masses | Obstruction theoryen
dc.titleComputational topology of equipartitions by hyperplanesen
dc.typeArticleen
dc.identifier.doi10.12775/TMNA.2015.004en
dc.identifier.scopus2-s2.0-84946833638en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage63en
dc.relation.lastpage90en
dc.relation.issue1en
dc.relation.volume45en
dc.description.rankM21-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeArticle-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0001-9801-8839-
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