Topology Atlas | Conferences

KNOTS in WASHINGTON XV (2nd Japan-USA Workshop in Knot Theory)
January 10-15, 2003
George Washington University and Johns Hopkins University
Washington, DC and Baltimore, MD, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Shin-ichi Suzuki, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

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Finite-type invariants based on doubled-delta moves
by
Ted Stanford
New Mexico State University
Coauthors: James Conant, Jacob Mostovoy

Given a move M (or set of moves) on knot or link diagrams, one can define finite-type invariants based on M. If M is a crossing change, then this is the usual notion of finite-type invariant. I will discuss invariants based on the doubled-delta move, which generates S-equivalence of knots (the equivalence generated by Seifert matrices). Some of the same results that one obtains in the usual case carry over to the doubled-delta case. For example, there is a theorem that says that the Ohyama-style definition of n-equivalence, which has been developed extensively by Gusarov and Habiro, gives the same equivalence classes of knots as the Vassiliev-style filtration on formal linear combinations of knots. Also, invariants based on doubled-delta moves are closely related to the loop filtration on chord diagrams introduced by Garoufalidis and Rozansky.

Date received: December 7, 2002

Copyright © 2002 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cajr-18.