On grid diagrams, braids and Markov moves

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.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2010

Author dc:creator

• Ayivor, Audry F

Advisor dc:contributor.advisor

• Gay, David T

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/12164

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/12164