More concordance homomorphisms from knot Floer homology

Categorical lifting of the Jones polynomial: a survey

“…Similar constructions have been given using other spectral sequences, including several infinite families of concordance invariants [155,106], though these are not known to be independent. (Again, these families were inspired by constructions in Heegaard Floer theory which, in that case, were shown to give a surjection from the smooth concordance group of topologically slice knots onto Z ∞ [133,39]. )…”

A further note on the concordance invariants epsilon and upsilon

“…Preliminaries. We assume the reader is familiar with knot Floer homology, defined by Ozsváth-Szabó [OS04a] and independently Rasmussen [Ras03], the ε-invariant, defined by Hom [Hom14a], the Υ-invariant, defined by Ozsváth-Stipsicz-Szabó [OSS17], and the ϕinvariant, defined by Dai-Hom-Stoffregen-Truong in [DHST19]. We briefly recall some properties for later use.…”

“…For any knot K, there are two recently defined invariants derived from knot Heegaard Floer theory: the Upsilon invariant, defined by Ozsváth-Stipsicz-Szabó in [OSS17], is a piecewise linear function on [0, 2] and denoted by Υ K (t); the phi invariant, defined by Dai-Hom-Stoffregen-Truong in [DHST19], is a sequence of integers and denoted by (ϕ j (K)) ∞ j=1 . These two invariants give homomorphisms from the smooth concordance group C to the abelian groups of continuous functions on [0, 2] and of sequences of integers (both with pointwise addition as the group operation), respectively.…”

Branched covers bounding rational homology balls

“…Further, K n is also strongly negative-amphichiral, which implies that it is rationally slice. Hence the τ -invariant [36], ε-invariant [18], Υ-invariant [37], Υ 2 -invariant [23], ν +invariant [19], ϕ j -invariants [9], and s-invariant [38] all vanish for K n . Moreover, since [K n ] ∈ ker ϕ, the sliceness obstructions from the Heegaard Floer correction term and Donaldsons diagonalization theorem (e.g.…”