L-space knots do not have essential Conway spheres- Tye Lidman (NC State)
Abstract: The properties of a knot are heavily governed by the essential surfaces that sit in the exterior. We will study a relation between essential planar surfaces in a knot exterior and knot Floer homology. This is joint work with Allison Moore (VCU) and Claudius Zibrowius (UBC).
Introduction to L-space links- Beibei Liu (Bonn)
Abstract: L-spaces are simplest 3-manifolds in terms of Heegaard Floer homology and L-space links are links such that all large surgeries are L-spaces. In this talk, we will concentrate 2-component L-space links which is a family of ``simple” links in the sense that their Alexander polynomials contain full information of the link Floer complex, and give explicit answers to questions relating to the link itself and its surgeries such as some detection results, sharp slice genus bounds and Thurston polytope.
Fibred knots, positivity and L-spaces- Filep Misev (Regensburg)
Abstract: Torus knots are lens space knots: they admit surgeries to lens spaces. This classical theorem has a modern analogue in terms of Floer homology: algebraic knots are L-space knots. I will present knots which do not admit L-space surgeries despite strikingly resembling algebraic knots and L-space knots in general. More precisely, we will see a method which allows to construct infinite families of knots of arbitrary fixed genus g > 1 which are all algebraically concordant to the torus knot T(2,2g+1) of the same genus and which are fibred and strongly quasipositive. Besides the study of L-spaces, these knots are of interest in the context of knot concordance, in particular Fox's slice-ribbon question, as well as Boileau-Rudolph's question, or Baker's conjecture, on the independence of strongly quasipositive fibred knots in the concordance group. Joint work with Gilberto Spano.
Non-left-orderable surgeries on iterated 1-bridge braids- Zipei Nie (Princeton)
Abstract: We prove that the L-space conjecture holds for those L-spaces obtained from Dehn surgery on knots which are closures of iterated 1-bridge braids, i.e., the braids obtained from satellite operations on 1-bridge braids. In the proof, we emphasize the power of fixed points in the Homeo_+(R) representation, and introduce property (D) to handle the satellite operation.