Скачать или смотреть Paula Truöl : Strongly quasipositive knots are concordant to infinitely many strongly QP knots

Knots are smooth embeddings of the (oriented) circle S^1 into the 3-sphere S^3, usually studied up to an equivalence relation called ambient isotopy. A natural generalization in dimension 4 of the question whether certain knots are isotopic to the trivial knot is the concept of concordance, another equivalence relation on the set of knots.

We show that every non-trivial strongly quasipositive knot is (smoothly) concordant to infinitely many pairwise non-isotopic strongly quasipositive knots. In contrast to our result, it was conjectured by Baker that concordant strongly quasipositive fibered knots are isotopic. Our construction uses a satellite operation whose companion is a slice knot with maximal Thurston-Bennequin number -1.


In the talk, we will define the relevant terms necessary to understand the theorem in the title, and explain the context of this result. If time permits, we will say a few words about how the construction extends to links.