Conjecture on orientation reversal for even-winding satellite patterns
Let be a pattern with winding number, the algebraic intersection number of the pattern with a meridional disk of the solid torus, a nonzero even integer. For a knot , write for the satellite knot obtained from and , and write for the inverse of in the smooth knot concordance group. Even-winding reversal conjecture. There exists a knot such that is not concordant to . No such example is known for even winding number unless the pattern induces the zero map, so the conjecture remains open.
References
Primary source
Randall Johanningsmeier, Hillary Kim and Allison N. Miller, “A partial resolution of Hedden's conjecture on satellite homomorphisms”, arXiv:2308.06890 (2023).
Progress summary
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.