The bipolar filtration of topologically slice knots

Slice knots and knot concordance

“…Theorem 4.15 ([CK21], see also [CHH13,CH15]). For each n, there is a subgroup of T n / T n+1 isomorphic to Z ∞ .…”

“…The proof of Theorem 4.15 combines von Neumann ρ-invariants with the Heegaard-Floer d-invariant. For more details, see [CHH13,CH15,CK21].…”

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“…Slicing knots in more general 4-manifolds has also been fruitful, e.g. in revealing structure within the knot concordance group [COT03, COT04, CT07, CHL09, CHL11], and in distinguishing between smooth concordance classes of topologically slice knots [CHH13,CH15,CK21]. In [MMP20] it was shown that the set of knots which bound smooth, null-homologous disks in a 4-manifold M can distinguish between smooth structures on M , that is, there are examples of homeomorphic smooth 4-manifolds M 1 , M 2 and a knot K ⊂ S 3 which bounds a smooth, null-homologous disk in M × 1 , but does not bound such a disk in M × 2 .…”