Rocha-Fontalvo, Yolima A.

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Khovanov homology for (3, k)-torus knots
(2016) Rocha-Fontalvo, Yolima A.; Ortiz-Navarro, Juan A.; College of Arts and Sciences - Sciences; Dziobiak, Stan; Romero, Juan; Department of Mathematics; Coutin, Sandra
This thesis studies the construction of Khovanov homology for (3, k)-torus knots by using combinatorial topology and skein theory, identifying common characteristics of Khovanov Bracket for (3, k)-torus knots. The r-th homology, Hr , of the complex C is calculated explicitly for r = 0, 1, 2k − 1 and 2k, it allows to obtain some exponents of the variables q and t in the graded Poincaré polynomial of the complex C, which is called the Khovanov bracket.