Characteristics of Graph Braid Groups

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dc.contributor.authorKo, Ki-Hyoungko
dc.contributor.authorPark, Hyo-Wonko
dc.date.accessioned2013-03-12T20:55:26Z-
dc.date.available2013-03-12T20:55:26Z-
dc.date.created2012-12-26-
dc.date.created2012-12-26-
dc.date.issued2012-12-
dc.identifier.citationDISCRETE & COMPUTATIONAL GEOMETRY, v.48, no.4, pp.915 - 963-
dc.identifier.issn0179-5376-
dc.identifier.urihttp://hdl.handle.net/10203/103487-
dc.description.abstractWe give formulae for the first homology of the n-braid group and the pure 2-braid group over a finite graph in terms of graph-theoretic invariants. As immediate consequences, a graph is planar if and only if the first homology of the n-braid group over the graph is torsion-free and the conjectures about the first homology of the pure 2-braid groups over graphs in Farber and Hanbury (arXiv:1005.2300 [math.AT]) can be verified. We discover more characteristics of graph braid groups: the n-braid group over a planar graph and the pure 2-braid group over any graph have a presentation whose relators are words of commutators, and the 2-braid group and the pure 2-braid group over a planar graph have a presentation whose relators are commutators. The latter was a conjecture in Farley and Sabalka (J. Pure Appl. Algebra, 2012) and so we propose a similar conjecture for higher braid indices.-
dc.languageEnglish-
dc.publisherSPRINGER-
dc.subjectCONFIGURATION-SPACE-
dc.subjectMORSE-THEORY-
dc.subject2 PARTICLES-
dc.subjectTOPOLOGY-
dc.titleCharacteristics of Graph Braid Groups-
dc.typeArticle-
dc.identifier.wosid000311503200005-
dc.identifier.scopusid2-s2.0-84870325516-
dc.type.rimsART-
dc.citation.volume48-
dc.citation.issue4-
dc.citation.beginningpage915-
dc.citation.endingpage963-
dc.citation.publicationnameDISCRETE & COMPUTATIONAL GEOMETRY-
dc.identifier.doi10.1007/s00454-012-9459-8-
dc.embargo.liftdate9999-12-31-
dc.embargo.terms9999-12-31-
dc.contributor.localauthorKo, Ki-Hyoung-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorBraid group-
dc.subject.keywordAuthorConfiguration space-
dc.subject.keywordAuthorGraph-
dc.subject.keywordAuthorHomology-
dc.subject.keywordAuthorPresentation-
dc.subject.keywordPlusCONFIGURATION-SPACE-
dc.subject.keywordPlusMORSE-THEORY-
dc.subject.keywordPlus2 PARTICLES-
dc.subject.keywordPlusTOPOLOGY-
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