On grid diagrams, braids and Markov moves

Master Thesis

2010

Permanent link to this Item
http://hdl.handle.net/11427/12164
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thesis_sci_2010_ayivor_a (1).pdf (1.46 MB)
Authors
Ayivor, Audry F
Supervisors
Gay, David T
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University of Cape Town

Department
Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
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Abstract
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 paper is to prove this fact. This result has already been proved by Cromwell [CrogS] and Dynnikov [Dyn06]. We present a new proof which is built upon Markov's theorem involving moves on braid words and link isotopy.
Description

Includes abstract.


Includes bibliographical references (leaves 42).

Keywords
Mathematics and Applied Mathematics

Reference:

Ayivor, A. 2010. On grid diagrams, braids and Markov moves. University of Cape Town.

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Masters