In mathematics, Khovanov homology is an oriented link invariant that arises as the cohomology of a cochain complex. It may be regarded as a categorification...
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He is known for introducing Khovanov homology for links, which was one of the first examples of categorification. Khovanov graduated from Moscow State...
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Jones polynomial (section Link with Khovanov homology)
Mikhail Khovanov constructed a certain chain complex for knots and links and showed that the homology induced from it is a knot invariant (see Khovanov homology)...
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Borel–Moore homology Cellular homology Cyclic homology Hochschild homology Floer homology Intersection homology K-homology Khovanov homology Morse homology Persistent...
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Cohomology (redirect from Extraordinary homology theory)
Flat cohomology Floer homology Galois cohomology Group cohomology Hochschild cohomology Intersection cohomology Khovanov homology Lie algebra cohomology...
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distinguish the unknot from all other knots, such as Khovanov homology and knot Floer homology. Other invariants can be defined by considering some integer-valued...
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invariant. (Their homologies satisfy similar formal properties to the combinatorially-defined Khovanov homology.) These homologies are closely related...
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research interests include knot theory, finite type invariants, and Khovanov homology. Bar-Natan earned his B.Sc. in mathematics at Tel Aviv University...
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known to be in both NP and co-NP. It is known that knot Floer homology and Khovanov homology detect the unknot, but these are not known to be efficiently...
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understand a concept in mathematics called Khovanov homology. Developed by Mikhail Khovanov around 2000, Khovanov homology provides a tool in knot theory, the...
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Sarkar 2009). Khovanov homology detects the unknot according to a result of Kronheimer and Mrowka. The complexity of Khovanov homology at least as high...
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{\displaystyle S} is constructed from f disjoint disks by attaching d bands. The homology group H 1 ( S ) {\displaystyle H_{1}(S)} is free abelian on 2g generators...
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Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial Alexander Bracket...
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Jones polynomial), and have been used in describing the properties of Khovanov homology with respect to tangle composition. Any subfactor planar algebra provides...
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Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial Alexander Bracket...
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the first homology (with integer coefficients) of X, denoted H 1 ( X ) {\displaystyle H_{1}(X)} . The transformation t acts on the homology and so we...
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polynomial has been shown to be related to Floer homology. The graded Euler characteristic of the knot Floer homology of Peter Ozsváth and Zoltan Szabó is the...
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others—studied knots from the point of view of the knot group and invariants from homology theory such as the Alexander polynomial. This would be the main approach...
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Mrowka. Jacob Rasmussen later gave a purely combinatorial proof using Khovanov homology, by means of the s-invariant. Kronheimer, P. B.; Mrowka, T. S. (1993)...
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Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial Alexander Bracket...
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Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial Alexander Bracket...
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characteristic of the Khovanov homology is equal to the original Jones polynomial. The generators for the chain complex of the Khovanov homology are states of...
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Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial Alexander Bracket...
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used in extending to tangles some properties of Jones polynomial and Khovanov homology of alternating links. An alternating planar algebra is an oriented...
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group Z; this follows because the abelianization agrees with the first homology group, which can be easily computed. The knot group (or fundamental group...
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understand a concept in mathematics called Khovanov homology. Developed by Mikhail Khovanov around 2000, Khovanov homology provides a tool in knot theory, the...
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doi:10.1016/j.ic.2013.03.007, S2CID 17127693 Bar-Natan, Dror (2005), "Khovanov's homology for tangles and cobordisms", Geom. Topol., 9 (3): 1443–1499, arXiv:math/0410495...
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Cobordism of Knots. Osaka J. Math. 3, p. 257–267, 1966. Jacob Rasmussen: Khovanov homology and the slice genus. Inv. Math. 182, p. 419–447, 2010. For the orientation...
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Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial Alexander Bracket...
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abelian groups by categorifying the notion of a Betti number. See also Khovanov homology as a knot invariant in knot theory. An example in finite group theory...
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