Khovanov Homology and Some of Its Applications in Knot Theory, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor) ; Eftekhary, Eaman (Co-Advisor)
Abstract
In this thesis, we study a homological invariant in Knot theory, called Khovanov homology. The main property of this invariants is that it gives us the Jones polynomial, as its graded Euler characteristic. Besides, the functor (1+1) TQFT, from the category of closed one-manifolds to the category of vector spaces is employed in its construction. By making some changes to this functor and defining another functor and some other steps, the so-called Lee spectral sequence is derived which starts from Khovanov homology and converges to another homological invariant of links, called Lee-Khovanov homology. Computation of this homology is very simple. By using this spectral sequence, a numerical...
Cataloging briefKhovanov Homology and Some of Its Applications in Knot Theory, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor) ; Eftekhary, Eaman (Co-Advisor)
Abstract
In this thesis, we study a homological invariant in Knot theory, called Khovanov homology. The main property of this invariants is that it gives us the Jones polynomial, as its graded Euler characteristic. Besides, the functor (1+1) TQFT, from the category of closed one-manifolds to the category of vector spaces is employed in its construction. By making some changes to this functor and defining another functor and some other steps, the so-called Lee spectral sequence is derived which starts from Khovanov homology and converges to another homological invariant of links, called Lee-Khovanov homology. Computation of this homology is very simple. By using this spectral sequence, a numerical...
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