Montoya-Vega, Gabriel

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Khovanov homology for almost alternating knots
(2017) Montoya-Vega, Gabriel; Ortiz-Navarro, Juan A.; College of Arts and Sciences - Sciences; Castellini, Gabriele; Romero-Oliveras, Juan; Department of Mathematics; Morell-Cruz, Luis
The large quantity of almost alternating knots gives rise to an important category in knot classification. We thus establish a result, previously given for the span of the bracket polynomial for almost alternating knots, in terms of the Jones polynomial. The Khovanov complex of a given knot K is generated by considering a planar projection of the knot with 2ⁿ states, each of which consists of a collection of simple closed curves in the plane. Following results in leading papers, we find which specific knots differ from others satisfying an equation and we present an alternative proof of a theorem related to the span of the Jones polynomial of an almost alternating knot; finally, keeping up our idea of finding invariants, we study their Khovanov homology.