A recursive formula for the Khovanov cohomology of a family of 3-stranded pretzel knots

After reviewing the process of associating graded cohomology groups (Khovanov cohomology) to a knot, we prove two lemmas that reduce the computational complexity of calculating the Khovanov cohomology. We then prove a recursive formula for the class of three-stranded pretzel knots P(-n,-m,m), where n and m are odd. This result shows that the rank of the Khovanov cohomology of P(-n-m,m) is an invariant of n.

Level thesis:degree_level

Master's Degree

Year dc:date.issued

2009

Author dc:creator

• Meier, Jeffrey

Advisor dc:contributor.advisor

• Jabuka, Stanislav

Committee members dc:contributor.committeemember

• Naik, Swatee
• Hoelzer, Guy

• Jones polynomial
• Khovanov cohomology
• Pretzel knots

Statement dc:rights

• In Copyright(All Rights Reserved)

Handle dc:identifier.uri

http://hdl.handle.net/11714/4077

OAI identifier oai:identifier

oai:scholarwolf.unr.edu:11714/4077