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Monodromy Action on Unknotting Tunnelsin Fiber Surfaces

Published online by Cambridge University Press:  20 November 2018

Jessica Banks  and
Matt Rathbun
Jessica Banks
Affiliation:
University of Hull, Hull, UK, HU6 7RX e-mail: jessica.banks@lmh.oxon.orgj.banks@hull.ac.uk
Matt Rathbun
Affiliation:
California State University, Fullerton, 800 N. State College Blvd., Fullerton, CA, 92831 e-mail: mrathbun@fullerton.edu
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Abstract

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In a 2012 paper, the second author showed that a tunnel of a tunnel number one, fibered link in ${{S}^{3}}$ 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.

Keywords

57M25fiberedmonodromytunnelclean
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 6 , 01 December 2016 , pp. 1201 - 1226
Copyright
Copyright © Canadian Mathematical Society 2016

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