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Showing 1 to 9 of 9 for “"Khovanov homology"”.
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Twisting bordered Khovanov homology
We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type D structure by adding a vertical type D structure which generalizes the vertical map in twisted tangle homology. One of the distinct advantages of our type D structure is that it is homotopy …
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Monopole Floer homology, link surgery, and odd Khovanov homology
… sequence for all versions of monopole Floer homology with mod 2 coefficients, generalizing the exact triangle. The spectral sequence begins with the monopole Floer homology of a hypercube of surgeries on a 3-manifold Y, and converges to the monopole Floer homology of Y itself. This allows one …
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Khovanov Homology & Uniqueness of Surfaces in the 4-ball
<p>We use the functoriality of Khovanov homology to examine the smooth, boundary-preserving isotopy of surfaces embedded in the 4-ball. We exemplify an infinite family of prime knots that bound an arbitrarily-large number of smoothly-distinct slice disks by distinguishing the maps they induce on …
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Khovanov Homology on Symmetric Unions of Certain 2-Bridge Knots
… by some invariants. In his 2000 paper, Mikhail Khovanov introduced a powerful new invariant, Khovanov Homology, which gives more information (an entire homology) than some more classic invariants. In this paper, we look at Khovanov Homology's ability to distinguish or classify symmetric unions …
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Results on spectral sequences for monopole and singular instanton Floer homologies
… to links, the singular instanton Floer homology introduced in [15] and the monopole Floer homology, which is explained in the book [16]. For both cases, we study in particular the spectral sequence that relates the Floer homologies to the Khovanov homologies of links. In our study of …
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Obstructions to slicing knots and splitting links
… in space-time. In the first half, we use Khovanov homology to the study the relationship between links in R3 and their components. We construct a new spectral sequence beginning at the Khovanov homology of a link and converging to the Khovanov homology of the split union of its components. …
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Relative Khovanov-Jacobsson Classes for Spanning Surfaces
<p>We define the Khovanov-Jacobsson class for a properly embedded surface in the 4-ball, an element of the Khovanov homology of its boundary link in the 3-sphere. We then develop general non-triviality criteria for Khovanov homology classes, and use these to distinguish the Khovanov-Jacobsson …
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Odd annular Bar-Natan Category and Gl(1|1)
… of the Lie superalgebra gl(1|1) on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and Wehrli in [7].</p>