Geodesic
Embedded annuli and Jones’ conjecture
LaFountain, Douglas J1 ; Menasco, William W2
1Department of Mathematics, Western Illinois University, Macomb, IL 61455, USA
2Department of Mathematics, University at Buffalo, Buffalo, NY 14260, USA
Algebraic and Geometric Topology, Tome 14 (2014) no. 6, pp. 3589-3601
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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.

DOI : 10.2140/agt.2014.14.3589
Classification : 57M25, 57R17, 20F36
Keywords: links, braids, braid foliations

LaFountain, Douglas J  1   ; Menasco, William W  2

1 Department of Mathematics, Western Illinois University, Macomb, IL 61455, USA
2 Department of Mathematics, University at Buffalo, Buffalo, NY 14260, USA 
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LaFountain, Douglas J; Menasco, William W. Embedded annuli and Jones’ conjecture. Algebraic and Geometric Topology, Tome 14 (2014) no. 6, pp. 3589-3601. doi: 10.2140/agt.2014.14.3589

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