Geometry and Topology Seminar: A 4-dimensional rational genus bound

Abstract: The minimal genus question asks: “What is the minimum genus of any surface representing a particular 2-dimensional homology class?” Historically, minimal genus questions have focused on 2-dimensional homology with integer coefficients. In this talk, we study a minimal genus question for homology classes with Q mod Z coefficients. We define the rational 4-genus of knots and present a lower bound in terms of Heegaard Floer tau invariants. Our bound also leads to Piecewise-Linear (PL) slice-genus bounds. This is joint work with Matthew Hedden.

Host: Minh Nguyen