A new generalization of the Khovanov homology

dc.contributor.author	Lee, Ik Jae
dc.date.accessioned	2012-08-10T13:12:41Z
dc.date.available	2012-08-10T13:12:41Z
dc.date.graduationmonth	August
dc.date.issued	2012-08-10
dc.date.published	2012
dc.description.abstract	In this paper we give a new generalization of the Khovanov homology. The construction begins with a Frobenius-algebra-like object in a category of graded vector-spaces with an anyonic braiding, with most of the relations weaken to hold only up to phase. The construction of Khovanov can be adapted to give a new link homology theory from such data. Both Khovanov's original theory and the odd Khovanov homology of Oszvath, Rassmusen and Szabo arise from special cases of the construction in which the braiding is a symmetry.
dc.description.advisor	David Yetter
dc.description.degree	Doctor of Philosophy
dc.description.department	Department of Mathematics
dc.description.level	Doctoral
dc.identifier.uri	http://hdl.handle.net/2097/14170
dc.language.iso	en_US
dc.publisher	Kansas State University
dc.rights	© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
dc.rights.uri	http://rightsstatements.org/vocab/InC/1.0/
dc.subject	Knot Theory
dc.subject	Topology
dc.subject.umi	Mathematics (0405)
dc.title	A new generalization of the Khovanov homology
dc.type	Dissertation

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