Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X-S Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically sharp volume bounds for weaving knots, and we prove that the infinite square weave is their geometric limit.
"Volume bounds for weaving knots." Algebr. Geom. Topol. 16 (6) 3301 - 3323, 2016. https://doi.org/10.2140/agt.2016.16.3301