Mathematics Colloquium



Department of Mathematics
University of Nebraska at Omaha


WHEN:
Wednesday, February 14, 2007 at 2:30 PM

WHERE:
Durham Science Center, Room 254

WHAT:


Robert Todd (Faculty Candidate)

University of Iowa


will give a talk on

Khovanov Homology and the Twist Number of Alternation Knots


ABSTRACT:
It has been shown that the sum of the absolute value of the second and penultimate coefficient of the Jones polynomial of an alternating knot is equal to the twist number of the knot. Here we give a new proof of this result using a variant of Khovanov’s homology that was defined by O. Viro for the Kauffman bracket. The proof is by induction on the number of crossings using the long exact sequence in Khovanov homology corresponding to the Kauffman bracket skein relation. 


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