Title: Non-complex cobordisms between quasipositive knots

 Abstract: 

Quasipositive knots occur in complex geometry as the transverse intersections of smooth algebraic curves in the complex affine plane with the 3-sphere. A complex cobordism is a surface that arises as the transverse intersection of such a smooth algebraic curve with the region bounded by two 4-balls of different radius with a common center. The two knots bounded by a complex cobordism are necessarily quasipositive, and every complex cobordism is necessarily optimal (defined in the talk). In 2016, Feller asked whether these two necessary conditions are also sufficient for the existence of a complex cobordism between two knots. In a joint work with Maciej Borodzik, we prove that they are not, for cobordisms of any genus. For genus 0, we extend our result to strongly quasipositive knots. In the talk, we will define the relevant terms and provide some context for our results.

https://www.unine.ch/math/seminaire-algebre-et-geometrie-de-neuchatel/