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# Monodromy Action on Unknotting Tunnels in Fiber Surfaces

Published:2016-06-23
Printed: Dec 2016
• Jessica Banks,
University of Hull, Hull, UK, HU6 7RX
• Matt Rathbun,
California State University, Fullerton, 800 N. State College Blvd., Fullerton, CA, 92831
 Format: LaTeX MathJax PDF

## Abstract

In \cite{RatTOFL}, 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: fibered, monodromy, tunnel, clean
 MSC Classifications: 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45}

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