dc.contributor.author Blagojevic, Pavle V. M. dc.contributor.author Blagojevic, Aleksandra dc.contributor.author Dimitrijevic McCleary, John dc.date.accessioned 2010-03-20T12:00:52Z dc.date.accessioned 2016-10-05T14:14:15Z dc.date.available 2010-03-20T12:00:52Z dc.date.available 2016-10-05T14:14:15Z dc.date.issued 2010-03-12 dc.identifier.uri http://publications.mfo.de/handle/mfo/1167 dc.description Research in Pairs 2009 en_US dc.description.abstract Algebraic 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. en_US 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. dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2010,08 dc.title Spectral Sequences in Combinatorial Geometry: Cheeses, Inscribed Sets, and Borsuk-Ulam Type Theorems en_US dc.type Preprint en_US dc.rights.license Dieses 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.license This 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.doi 10.14760/OWP-2010-08 local.scientificprogram Research in Pairs 2009 local.series.id OWP-2010-08 dc.identifier.urn urn:nbn:de:101:1-20100601391 dc.identifier.ppn 1649520018
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