Department of Mathematics - Master Calendar

Abstract: In 2022 Agol showed ribbon concordance gives a partial ordering on knots, confirming a conjecture of Gordon from 1981. Gordon also conjectured that there are no infinite descending chains under this order. We prove that any knot has finitely many fibered predecessors under ribbon concordance; in particular any fibered knot has finitely many predecessors, implying Gordon’s conjecture for fibered knots. This is joint work with Baldwin and Sivek and builds on their recent work showing any knot has finitely many fibered hyperbolic predecessors. The key new input for removing the word “hyperbolic” is a rank inequality for knot Floer homology of satellites, which is of independent interest. We prove this rank inequality using the immersed curve interpretation of bordered Floer homology.