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Monodromy action on unknotting tunnels in fiber surfaces

Banks, Jessica; Rathbun, Matt


Jessica Banks

Matt Rathbun


The second author showed that a tunnel of tunnel number one, fibered link in S³ can be isotoped to lie as a properly embedded arc in the fiber surface of the link. In this paper, we observe that this is true for fibered links in any 3-manifold, we analyze how the arc behaves under the monodromy action, and we show that the tunnel arc is nearly clean, with the possible exception of twisting around the boundary of the fiber.


Banks, J., & Rathbun, M. (2016). Monodromy action on unknotting tunnels in fiber surfaces. Canadian journal of mathematics = Journal canadien de mathématiques, 68(6), 1201-1226.

Journal Article Type Article
Acceptance Date Nov 23, 2015
Online Publication Date Jun 23, 2016
Publication Date Dec 1, 2016
Deposit Date Dec 21, 2015
Publicly Available Date Nov 23, 2017
Journal Canadian journal of mathematics
Print ISSN 0008-414X
Electronic ISSN 1496-4279
Publisher Canadian Mathematical Society
Peer Reviewed Peer Reviewed
Volume 68
Issue 6
Pages 1201-1226
Keywords Monodromy; Fibered; Tunnel; Clean
Public URL
Publisher URL
Additional Information Authors' accepted manuscript of article published in: Canadian Journal of Mathematics, 2016, v.68.


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