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Monodromy action on unknotting tunnels in fiber surfaces

Banks, Jessica; Rathbun, Matt

Authors

Jessica Banks

Matt Rathbun

Abstract

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.

Journal Article Type Article
Publication Date Dec 1, 2016
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
Institution Citation 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. https://doi.org/10.4153/CJM-2016-002-1
DOI https://doi.org/10.4153/CJM-2016-002-1
Keywords Monodromy; Fibered; Tunnel; Clean
Publisher URL http://cms.math.ca/10.4153/CJM-2016-002-1
Additional Information Authors' accepted manuscript of article published in: Canadian Journal of Mathematics, 2016, v.68.

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