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dc.contributor.authorBlagojevic, Pavle V. M.
dc.contributor.authorBlagojevic, Aleksandra
dc.contributor.authorDimitrijevic McCleary, John
dc.date.accessioned2010-03-20T12:00:52Z
dc.date.accessioned2016-10-05T14:14:15Z
dc.date.available2010-03-20T12:00:52Z
dc.date.available2016-10-05T14:14:15Z
dc.date.issued2010-03-12
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1167
dc.descriptionResearch in Pairs 2009en_US
dc.description.abstractAlgebraic topological methods are especially suited to determining the nonexistence 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 $\mathbb{R}^m$ in which a subspace, a discriminant, often an arrangement of linear subspaces $\mathcal{A}$, expresses a desirable condition on the configurations. Add symmetries of all these data under a group $G$ for which the mapping is equivariant. Removing the discriminant leads to the problem of the existence of an equivariant mapping from $X$ to $\mathbb{R}^m$- the discriminant. Algebraic topology may be applied to show that no such mapping exists, and hence 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 $\mathbb{R}^d$, 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 nonexistence of equivariant maps which generalizes the Borsuk-Ulam theorem.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2010,08
dc.titleSpectral Sequences in Combinatorial Geometry: Cheeses, Inscribed Sets, and Borsuk-Ulam Type Theoremsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2010-08
local.scientificprogramResearch in Pairs 2009
local.series.idOWP-2010-08
dc.identifier.urnurn:nbn:de:101:1-20100601391
dc.identifier.ppn1649520018


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