The infimum, supremum, and geodesic length of a braid conjugacy class

Cited 29 time in webofscience Cited 0 time in scopus
  • Hit : 1243
  • Download : 0
DC FieldValueLanguage
dc.contributor.authorBirman, JSko
dc.contributor.authorKo, Ki-Hyoungko
dc.contributor.authorLee, SJko
dc.date.accessioned2013-03-03T12:36:25Z-
dc.date.available2013-03-03T12:36:25Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2001-12-
dc.identifier.citationADVANCES IN MATHEMATICS, v.164, no.1, pp.41 - 56-
dc.identifier.issn0001-8708-
dc.identifier.urihttp://hdl.handle.net/10203/78699-
dc.description.abstractAlgorithmic solutions to the conjugacy problem in the braid groups B-n, n = 2, 3, 4,... were given in earlier work. This note concerns the computation of two integer class invariants, known as "inf" and "sup." A key issue in both algorithms is the number m of times one must "cycle" (resp. "decycle") in order to either increase inf (resp. decrease sup) or to be sure that it is already maximal (resp. minimal) for the class. Our main result is to prove that m is bounded above by ((n(2) - n)/2) - I in the situation stated by E. A. Elrifai and H. R. Morton (1994, Quart. J. Math. Oxford 45, 479-497) and by n - 2 in the situation stated by authors (1998, Adv. Math. 139, 322-353). It follows immediately that the computation of inf and sup is polynomial in both word length and braid index, in both algorithms. The integers inf and sup determine (but are not determined by) the shortest geodesic length for elements in a conjugacy class, and so we also obtain a polynomial-time algorithm for computing this length. (C) 2001 Elsevier Science.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.titleThe infimum, supremum, and geodesic length of a braid conjugacy class-
dc.typeArticle-
dc.identifier.wosid000173051800003-
dc.identifier.scopusid2-s2.0-0035684713-
dc.type.rimsART-
dc.citation.volume164-
dc.citation.issue1-
dc.citation.beginningpage41-
dc.citation.endingpage56-
dc.citation.publicationnameADVANCES IN MATHEMATICS-
dc.contributor.localauthorKo, Ki-Hyoung-
dc.contributor.nonIdAuthorBirman, JS-
dc.contributor.nonIdAuthorLee, SJ-
dc.type.journalArticleArticle-
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 29 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0