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Dec 22, 2021 at 7:54 comment added Lukas Lewark The statement that "the bridge number of a given link equals the minimal number of meridian generators of its group" is known as the meridional rank conjecture. See e.g. dx.doi.org/10.4310/CAG.2020.v28.n2.a2
Mar 31, 2015 at 3:32 comment added Ian Agol Chris Cornwell obtained lower bounds on the meridional rank of certain pretzel knots, showing they are equal to the bridge number: arxiv.org/abs/1303.4943
Oct 9, 2013 at 4:30 comment added dvitek This is also problem 1.11 in Kirby's list, attributed therein to Cappell and Shaneson.
Jul 25, 2012 at 4:05 history answered Makoto Ozawa CC BY-SA 3.0