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dc.contributor.authorKauffman, Louis H.
dc.contributor.authorManturov, Vassily Olegovich
dc.date.accessioned2015-07-31T12:00:00Z
dc.date.accessioned2016-10-05T14:14:02Z
dc.date.available2015-07-31T12:00:00Z
dc.date.available2016-10-05T14:14:02Z
dc.date.issued2015-07-31
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1101
dc.descriptionResearch in Pairs 2014en_US
dc.description.abstractWe construct graph-valued analogues of the Kuperberg sl(3) and $G_2$ invariants for virtual knots. The restriction of the sl(3) and $G_2$ invariants for classical knots coincides with the usual Homflypt sl(3) invariant and $G_2$ invariants. For virtual knots and graphs these invariants provide new graphical information that allows one to prove minimality theorems and to construct new invariants for free knots (unoriented and unlabeled Gauss codes taken up to abstract Reidemeister moves). A novel feature of this approach is that some knots are of sufficient complexity that they evaluate themselves in the sense that the invariant is the knot itself seen as a combinatorial structure. The paper generalizes these structures to virtual braids and discusses the relationship with the original Penrose bracket for graph colorings.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2015,13
dc.subjectKnoten_US
dc.subjectlinken_US
dc.subjectvirtual knoten_US
dc.subjectgraphen_US
dc.subjectinvarianten_US
dc.subjectKuperberg sl(3) bracketen_US
dc.subjectKuperberg C2 bracketen_US
dc.subjectKuperberg G_2 bracketen_US
dc.subjectquantum invarianten_US
dc.titleGraphical constructions for the sl(3), C2 and G2 invariants for virtual knots, virtual braids and free knotsen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2015-13
local.scientificprogramResearch in Pairs 2014
local.series.idOWP-2015-13
local.subject.msc57
dc.identifier.urnurn:nbn:de:101:1-2015073031218
dc.identifier.ppn1657471829


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