Realization Spaces of Arrangements of Convex Bodies

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dc.contributor.authorDobbins, Michael Geneko
dc.contributor.authorHolmsen, Andreasko
dc.contributor.authorHubard, Alfredoko
dc.date.accessioned2017-07-18T05:42:21Z-
dc.date.available2017-07-18T05:42:21Z-
dc.date.created2017-07-03-
dc.date.created2017-07-03-
dc.date.issued2017-07-
dc.identifier.citationDISCRETE & COMPUTATIONAL GEOMETRY, v.58, no.1, pp.1 - 29-
dc.identifier.issn0179-5376-
dc.identifier.urihttp://hdl.handle.net/10203/224774-
dc.description.abstractWe introduce combinatorial types of planar arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our main results witness a trade-off between the combinatorial complexity of the bodies and the topological complexity of their realization space. First, we show that every combinatorial type is realizable and its realization space is contractible under mild assumptions. Second, we prove a universality theorem that says the restriction of the realization space to arrangements polygons with a bounded number of vertices can have the homotopy type of any primary semialgebraic set.-
dc.languageEnglish-
dc.publisherSPRINGER-
dc.subjectORIENTED MATROIDS-
dc.subjectORDER TYPES-
dc.subjectCONFIGURATIONS-
dc.subjectSETS-
dc.subjectPOLYTOPES-
dc.subjectFAMILIES-
dc.subjectPLANE-
dc.titleRealization Spaces of Arrangements of Convex Bodies-
dc.typeArticle-
dc.identifier.wosid000403080400001-
dc.identifier.scopusid2-s2.0-85015155130-
dc.type.rimsART-
dc.citation.volume58-
dc.citation.issue1-
dc.citation.beginningpage1-
dc.citation.endingpage29-
dc.citation.publicationnameDISCRETE & COMPUTATIONAL GEOMETRY-
dc.identifier.doi10.1007/s00454-017-9869-8-
dc.contributor.localauthorHolmsen, Andreas-
dc.contributor.nonIdAuthorDobbins, Michael Gene-
dc.contributor.nonIdAuthorHubard, Alfredo-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorConvexity-
dc.subject.keywordAuthorOriented matroid-
dc.subject.keywordAuthorChirotope-
dc.subject.keywordAuthorRealization space-
dc.subject.keywordPlusORIENTED MATROIDS-
dc.subject.keywordPlusORDER TYPES-
dc.subject.keywordPlusCONFIGURATIONS-
dc.subject.keywordPlusSETS-
dc.subject.keywordPlusPOLYTOPES-
dc.subject.keywordPlusFAMILIES-
dc.subject.keywordPlusPLANE-
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