We study the asymptotics of a family of link invariants on the orbits of a smooth volume-preserving ergodic vector field on a compact domain of the 3-space. These invariants, called linear saddle invariants, include many concordance invariants and generate an infinite-dimensional vector space of link invariants. In contrast, the vector space of asymptotic linear saddle invariants is 1-dimensional, generated by the asymptotic signature. We also determine the asymptotic slice genus and relate it to the asymptotic signature.
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Sebastian Baader, Asymptotic concordance invariants for ergodic vector fields. Comment. Math. Helv. 86 (2011), no. 1, pp. 1–12DOI 10.4171/CMH/215