Link cobordisms and absolute gradings on link Floer homology

  • Ian Zemke

    Princeton University, USA
Link cobordisms and absolute gradings on link Floer homology cover
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Abstract

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 new bound for 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 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.

Cite this article

Ian Zemke, Link cobordisms and absolute gradings on link Floer homology. Quantum Topol. 10 (2019), no. 2, pp. 207–323

DOI 10.4171/QT/124