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The Jones-Kauffman Polynomial and the Bollob'as-Riordan Polynomial

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Dr. Xian'an Jin, Xi'amen University, China

What
  • Colloquium
  • Topology Seminar
When Thu, Oct 20, 2011
from 01:00 PM to 02:00 PM
Where Ritter Hall 30
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Abstract: In this talk, we first construct a signed ribbon graph for an arbitrary virtual link diagram based on its graphical checkerboard coloring and contractions for all twisted bands corresponding to virtual crossings.  Then we build a relation between the Kauffman bracket polynomial of a virtual link diagram and Bollob'as-Riordan polynomial of the signed ribbon graph described above.  Finally we prove that this relation is an extension of the famous result of Kauffman's (hence, Thistlethwaite's) on the connection between the Kauffman bracket polynomial of classical link diagrams and the Tutte polynomial of corresponding signed checkerboard graphs.

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