More concordance homomorphisms from knot Floer homology

Dai, Irving¹ ; Hom, Jennifer² ; Stoffregen, Matthew³ ; Truong, Linh⁴

¹ Department of Mathematics, Princeton University, Princeton, NJ, United States, Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States
² School of Mathematics, Georgia Institute of Technology, Atlanta, GA, United States
³ Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States
⁴ Department of Mathematics, Columbia University, New York, NY, United States, School of Mathematics, Institute for Advanced Study, Princeton, NJ, United States

Geometry & topology, Tome 25 (2021) no. 1, pp. 275-338.

Résumé

We define an infinite family of linearly independent, integer-valued smooth concordance homomorphisms. Our homomorphisms are explicitly computable and rely on local equivalence classes of knot Floer complexes over the ring $\mathbb{𝔽}\left[U,V\right]∕\left(UV=0\right)$. We compare our invariants to other concordance homomorphisms coming from knot Floer homology, and discuss applications to topologically slice knots, concordance genus and concordance unknotting number.

Détail

DOI : 10.2140/gt.2021.25.275

Classification : 57M25, 57N70, 57R58
Keywords: concordance, knots, knot Floer homology

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