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  4. Khovanov同調群的研究
 
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Khovanov同調群的研究

Some computations of Khovanov Homology

Date Issued
2005
Date
2005
Author(s)
Liao, Chiun-Ming
DOI
en-US
URI
http://ntur.lib.ntu.edu.tw//handle/246246/59507
Abstract
A new link invariant found by Khovanov is a mysterious invariant. The brief idea is to build a chain complex for a knot so that its Euler characteristic is its Jones polynomial, and we can compute the Khovanov homology for this chain complex. It is a link invariant, but the meaning of the terms in it is not yet varified. Instead some masters drill out many properties inside this invariant. One amazing property of the Khovanov homology of prime alternative knots is stated in Dror Bar-Natan's paper and is proved by Eun Soo Lee. It says that the Khovanov homology of prime alternative knots appears only in two skew parallel lines if we draw them in a table. In this article I want to find some relationship between connected sum and disjoint union of two knots. In Knovanov's paper he introduce a nice relation between connected sum and disjoint union of two knots. It is long exact sequences, and my computation is relied on it. The program released by Dror Bar-Natan really does great help to me.
Subjects
同調群
Khovanov
homology
knot
Type
thesis
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ntu-94-R92221013-1.pdf

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