Abstract
We show that after stabilizations of opposite parity and braid isotopy, any two braids in the same topological link type cobound embedded annuli. We use this to prove the generalized Jones’ conjecture relating the braid index and algebraic length of closed braids within a link type, following a reformulation of the problem by Kawamuro.
Citation
Douglas J LaFountain. William W Menasco. "Embedded annuli and Jones' conjecture." Algebr. Geom. Topol. 14 (6) 3589 - 3601, 2014. https://doi.org/10.2140/agt.2014.14.3589
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