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Showing 1 to 4 of 4 for “"Grid diagrams"”.
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On grid diagrams, braids and Markov moves
Grid diagrams are essential in the new combinatorial version [MOST07] of the Heegaard Floer knot homology, and proving that these homologies are actually knot and link invariants depends on knowing that two grid diagrams representing isotopic links are related by grid moves. The purpose of this …
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Crossing Number Bounds of Mosaic Knot Diagrams
… some previously undocumented link mosaic diagrams. Next we prove an upper and lower bound on crossing number of certain mosaic diagrams of knots in terms of winding number for knot diagrams that make only counterclockwise turns. Next we begin drawing mosaic diagrams that have a more …
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Knot Floer Homology and Categorification
… of invariance that does not depend on Heegaard diagrams, holomorphic disks, or grid diagrams. Then, taking Khovanov's HOMFLY-PT homology as our model, we define a category of twisted Soergel bimodules and construct a braid group action on the homotopy category of complexes of twisted Soergel …
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The Maximal Thurston-Bennequin Number on Grid Number n Diagrams
… of Legendrian knots and links on a rectangular grid with arc index n.</p> <p>TB(n)=CR(n)-[n/2]</p> <p>In order to prove the bound, we will separate our work for when n is even and when n is odd. After we prove the upper bound, we will show that there are unique knots and links on each grid which …