DC Field | Value | Language |
---|---|---|
dc.contributor.author | Ko, Ki-Hyoung | ko |
dc.contributor.author | Park, Hyo-Won | ko |
dc.date.accessioned | 2013-03-12T20:55:26Z | - |
dc.date.available | 2013-03-12T20:55:26Z | - |
dc.date.created | 2012-12-26 | - |
dc.date.created | 2012-12-26 | - |
dc.date.issued | 2012-12 | - |
dc.identifier.citation | DISCRETE & COMPUTATIONAL GEOMETRY, v.48, no.4, pp.915 - 963 | - |
dc.identifier.issn | 0179-5376 | - |
dc.identifier.uri | http://hdl.handle.net/10203/103487 | - |
dc.description.abstract | We 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.language | English | - |
dc.publisher | SPRINGER | - |
dc.subject | CONFIGURATION-SPACE | - |
dc.subject | MORSE-THEORY | - |
dc.subject | 2 PARTICLES | - |
dc.subject | TOPOLOGY | - |
dc.title | Characteristics of Graph Braid Groups | - |
dc.type | Article | - |
dc.identifier.wosid | 000311503200005 | - |
dc.identifier.scopusid | 2-s2.0-84870325516 | - |
dc.type.rims | ART | - |
dc.citation.volume | 48 | - |
dc.citation.issue | 4 | - |
dc.citation.beginningpage | 915 | - |
dc.citation.endingpage | 963 | - |
dc.citation.publicationname | DISCRETE & COMPUTATIONAL GEOMETRY | - |
dc.identifier.doi | 10.1007/s00454-012-9459-8 | - |
dc.embargo.liftdate | 9999-12-31 | - |
dc.embargo.terms | 9999-12-31 | - |
dc.contributor.localauthor | Ko, Ki-Hyoung | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Braid group | - |
dc.subject.keywordAuthor | Configuration space | - |
dc.subject.keywordAuthor | Graph | - |
dc.subject.keywordAuthor | Homology | - |
dc.subject.keywordAuthor | Presentation | - |
dc.subject.keywordPlus | CONFIGURATION-SPACE | - |
dc.subject.keywordPlus | MORSE-THEORY | - |
dc.subject.keywordPlus | 2 PARTICLES | - |
dc.subject.keywordPlus | TOPOLOGY | - |
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