On slice-torus invariants and applications.
Carlo Collari (Firenze)
Monday 26th November, 2018 16:00-17:00 Maths 311B
With the advent of knot homology theories, such as Khovanov and knot Floer homologies, new invariants to study knot concordance have been developed. For example, Rasmussen's s-invariant, the Ozsvath-Szabo tau-invariant and the s_N invariants due to Lobb and Wu, independently, and another family of invariants introduced by Lewark and Lobb. All these invariants share three fundamental properties, which were first identified by Livingston, and were called ''slice-torus
invariants'' by Lewark. Some among the slice-torus invariants, namely s, tau and the s_N's admit a generalisation to strong concordance invariants for links. Motivated by the properties shared by these extensions, together with A. Cavallo (Max Planck, Bonn), we gave the definition of slice-torus
link invariants and studied their properties.
In this talk I will give the definition of slice-torus link invariant, and describe some of their properties. Finally, I will also give some applications and define some new strong concordance invariants using
the Whitehead doubling.