On the Goussarov-Polyak-Viro Finite-Type Invariants and the Virtualization Move
Abstract
In this paper, it is shown that there are no nonconstant Goussarov-Polyak-Viro finite-type invariants that are invariant under the virtualization move. As an immediate corollary, we obtain the theorem which states none of the Birman coefficients of the Jones-Kauffman polynomial are of GPV finite type.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2010
- DOI:
- arXiv:
- arXiv:1001.2247
- Bibcode:
- 2010arXiv1001.2247C
- Keywords:
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- Mathematics - Geometric Topology;
- 57M25;
- 57M27