Monodromy action on unknotting tunnels in fiber surfaces

Banks, Jessica; Rathbun, Matt

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.

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

• 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
• Publisher: Canadian Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 68
• Issue: 6
• Pages: 1201-1226
• DOI: https://doi.org/10.4153/CJM-2016-002-1
• Keywords: Monodromy; Fibered; Tunnel; Clean
• Public URL: https://hull-repository.worktribe.com/output/383265
• 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.
• Contract Date: Nov 23, 2017