Classical And Virtual Pseudodiagram Theory And New Bounds On Unknotting Numbers And Genus

Title:
Classical And Virtual Pseudodiagram Theory And New Bounds On Unknotting Numbers And Genus
Authors:
Henrich, A.; MacNaughton, N.; Narayan, Sivaram K.; Pechenik, O.; Townsend, J.
Abstract:
A pseudodiagram is a diagram of a knot with some crossing information missing. We review and expand the theory of pseudodiagrams introduced by Hanaki. We then extend this theory to the realm of virtual knots, a generalization of knots. In particular, we analyze the trivializing number of a pseudodiagram, i.e. the minimum number of crossings that must be resolved to produce the unknot. We consider how much crossing information is needed in a virtual pseudodiagram to identify a non-trivial knot, a classical knot, or a non-classical knot. We then apply pseudodiagram theory to develop new upper bounds on unknotting number, virtual unknotting number, and genus.
Citation:
Henrich, A., N. MacNaughton, S. Narayan, O. Pechenik, et al. 2011. "Classical And Virtual Pseudodiagram Theory And New Bounds On Unknotting Numbers And Genus." Journal Of Knot Theory And Its Ramifications 20(4): 625-650.
Publisher:
World Scientific Publishing
DATE ISSUED:
2011-04
Department:
Mathematics
Type:
article
PUBLISHED VERSION:
10.1142/S0218216511009388
PERMANENT LINK:
http://hdl.handle.net/11282/310109

Full metadata record

DC FieldValue Language
dc.contributor.authorHenrich, A.en_US
dc.contributor.authorMacNaughton, N.en_US
dc.contributor.authorNarayan, Sivaram K.en_US
dc.contributor.authorPechenik, O.en_US
dc.contributor.authorTownsend, J.en_US
dc.date.accessioned2013-12-23T16:25:35Z-
dc.date.available2013-12-23T16:25:35Z-
dc.date.issued2011-04en
dc.identifier.citationHenrich, A., N. MacNaughton, S. Narayan, O. Pechenik, et al. 2011. "Classical And Virtual Pseudodiagram Theory And New Bounds On Unknotting Numbers And Genus." Journal Of Knot Theory And Its Ramifications 20(4): 625-650.en_US
dc.identifier.issn0218-2165en_US
dc.identifier.urihttp://hdl.handle.net/11282/310109-
dc.description.abstractA pseudodiagram is a diagram of a knot with some crossing information missing. We review and expand the theory of pseudodiagrams introduced by Hanaki. We then extend this theory to the realm of virtual knots, a generalization of knots. In particular, we analyze the trivializing number of a pseudodiagram, i.e. the minimum number of crossings that must be resolved to produce the unknot. We consider how much crossing information is needed in a virtual pseudodiagram to identify a non-trivial knot, a classical knot, or a non-classical knot. We then apply pseudodiagram theory to develop new upper bounds on unknotting number, virtual unknotting number, and genus.en_US
dc.publisherWorld Scientific Publishingen_US
dc.identifier.doi10.1142/S0218216511009388-
dc.subject.departmentMathematicsen_US
dc.titleClassical And Virtual Pseudodiagram Theory And New Bounds On Unknotting Numbers And Genusen_US
dc.typearticleen_US
dc.identifier.journalJournal Of Knot Theory And Its Ramificationsen_US
dc.subject.keywordPseudodiagramsen_US
dc.subject.keywordVirtual knotsen_US
dc.subject.keywordUnknotting numberen_US
dc.subject.keywordGenusen_US
dc.identifier.volume20en_US
dc.identifier.issue4en_US
dc.identifier.startpage625en_US
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