Greene's branched-double-cover conjecture for alternating links
Let and be links whose branched double covers are homeomorphic.
Greene's conjecture. If a pair of links have homeomorphic branched double-covers, then either both are alternating or both are non-alternating.
This conjecture concerns whether alternation is determined by the homeomorphism type of a link's branched double cover. The source attributes the conjecture to Greene and gives no resolution, so its status remains open.
References
Primary source
Hamid Abchir and Mohammed Sabak, “Infinite families of non-left-orderable L-spaces”, arXiv:2104.14930 (2021).
Additional references
2 papers in this index state this conjecture (2011–2021). The statement above is taken from the most recent of them; the others are arXiv:1103.0487.
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.