Abstract
For every –component ribbon link we prove that the Jones polynomial is divisible by the polynomial of the trivial link. This integrality property allows us to define a generalized determinant , for which we derive congruences reminiscent of the Arf invariant: every ribbon link satisfies modulo , whence in particular modulo .
These results motivate to study the power series expansion at , instead of as usual. We obtain a family of link invariants , starting with the link determinant obtained from a Seifert surface spanning . The invariants are not of finite type with respect to crossing changes of , but they turn out to be of finite type with respect to band crossing changes of . This discovery is the starting point of a theory of surface invariants of finite type, which promises to reconcile quantum invariants with the theory of Seifert surfaces, or more generally ribbon surfaces.
Citation
Michael Eisermann. "The Jones polynomial of ribbon links." Geom. Topol. 13 (2) 623 - 660, 2009. https://doi.org/10.2140/gt.2009.13.623
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