Volume 9, issue 1 (2009)

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Cabling sequences of tunnels of torus knots

Sangbum Cho and Darryl McCullough

Algebraic & Geometric Topology 9 (2009) 1–20

In previous work, we developed a theory of tunnels of tunnel number 1 knots in S3. It yields a parameterization in which each tunnel is described uniquely by a finite sequence of rational parameters and a finite sequence of 0s and 1s, that together encode a procedure for constructing the knot and tunnel. In this paper we calculate these invariants for all tunnels of torus knots

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knot, link, tunnel, torus knot
Mathematical Subject Classification 2000
Primary: 57M25
Received: 5 August 2008
Revised: 22 October 2008
Accepted: 11 December 2008
Published: 5 January 2009
Sangbum Cho
University of California at Riverside
Department of Mathematics
California 92521
Darryl McCullough
University of Oklahoma
Department of Mathematics
Oklahoma 73019-3103