We show that the link cobordism maps defined by the author are graded and satisfy a grading change formula. Using the grading change formula, we prove a newbound for ‡K.t/for knot cobordisms in negative definite 4-manifolds. As another application, we show that the link cobordism maps associated to a connected, closed surface in S4 are determined by the genus of the surface. We also prove a new adjunction relation and adjunction inequality for the link cobordism maps. Along the way, we see how many known results in Heegaard Floer homology can be proven using basic properties of the link cobordism maps, together with the grading change formula.
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Geometry and Topology
- Heegaard Floer homology
- Knotted surfaces