The tau-sharp equality conjecture for knots

About 6 years old · traced to

Let K⊂S3K\subset S^3 be a knot. The invariant τ♯\tau^\sharp is the framed-instanton concordance homomorphism, and τ\tau is the Heegaard Floer concordance invariant.

Tau-sharp equality conjecture.

τ♯(K)=τ(K)\tau^\sharp(K)=\tau(K)

for every knot K⊂S3K\subset S^3.

The source states that the two concordance homomorphisms agree for homogeneous and quasipositive knots, and conjectures equality for all knots. No resolution is given here.

References

Primary source

John A. Baldwin and Steven Sivek, “Framed instanton homology and concordance”, arXiv:2004.08699 (2021).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.