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dc.contributor.authorBlagojević, Pavleen
dc.contributor.authorDimitrijević-Blagojević, Aleksandraen
dc.contributor.authorMcCleary, Johnen
dc.date.accessioned2020-04-26T19:36:33Z-
dc.date.available2020-04-26T19:36:33Z-
dc.date.issued2011-09-15en
dc.identifier.issn0166-8641en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/573-
dc.description.abstractAlgebraic topological methods are especially well suited for determining the non-existence of continuous mappings satisfying certain properties. In combinatorial problems it is sometimes possible to define a mapping from a space X of configurations to a Euclidean space Rm in which a subspace, a discriminant, often an arrangement of linear subspaces A, expresses a target condition on the configurations. Add symmetries of all these data under a group G for which the mapping is equivariant. If we remove the discriminant from Rm, we can pose the problem of the existence of an equivariant mapping from X to the complement of the discriminant in Rm. Algebraic topology may sometimes be applied to show that no such mapping exists, and hence the image of the original equivariant mapping must meet the discriminant. We introduce a general framework, based on a comparison of Leray-Serre spectral sequences. This comparison can be related to the theory of the Fadell-Husseini index. We apply the framework to: •solve a mass partition problem (antipodal cheeses) in Rd, •determine the existence of a class of inscribed 5-element sets on a deformed 2-sphere, •obtain two different generalizations of the theorem of Dold for the non-existence of equivariant maps which generalizes the Borsuk-Ulam theorem.en
dc.publisherElsevier-
dc.relationEuropean Union’s Seventh Framework Programme (FP7/2007–2013)/ERC, Grant agreement No. 247029-SDModels-
dc.relationAdvanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security-
dc.relation.ispartofTopology and its Applicationsen
dc.subjectBorel construction | Borsuk-Ulam type theorems | Equivariant cohomology | Mass partition problems | Serre spectral sequence | Subspace arrangementsen
dc.titleSpectral sequences in combinatorial geometry: Cheeses, inscribed sets, and Borsuk-Ulam type theoremsen
dc.typeArticleen
dc.identifier.doi10.1016/j.topol.2011.06.035en
dc.identifier.scopus2-s2.0-79961172194en
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Arts-
dc.relation.firstpage1920en
dc.relation.lastpage1936en
dc.relation.issue15en
dc.relation.volume158en
dc.description.rankM23-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0003-3649-9897-
crisitem.project.projectURLhttp://www.mi.sanu.ac.rs/novi_sajt/research/projects/174008e.php-
crisitem.project.fundingProgramDirectorate for Education & Human Resources-
crisitem.project.openAireinfo:eu-repo/grantAgreement/NSF/Directorate for Education & Human Resources/1740089-
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