Meridional almost normal surfaces in knot complements

Wilson, Robin

doi:10.2140/agt.2008.8.1717

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Meridional almost normal surfaces in knot complements

Robin Todd Wilson

Algebraic & Geometric Topology 8 (2008) 1717–1740

DOI: 10.2140/agt.2008.8.1717

Abstract

Suppose $K$ is a knot in a closed 3–manifold $M$ such that $M - N (K)$ is irreducible. We show that for any integer $n$ there exists a triangulation of $M - N (K)$ such that any weakly incompressible bridge surface for $K$ of $n$ bridges or fewer is isotopic to an almost normal bridge surface.

Keywords

normal surface, Heegaard surface, bridge position, strongly irreducible, weakly incompressible

Mathematical Subject Classification 2000

Primary: 57M99

References

Publication

Received: 6 October 2007

Accepted: 1 September 2008

Published: 8 October 2008

Authors

Robin Todd Wilson
Department of Mathematics and Statistics California State Polytechnic University Pomona 3801 West Temple Ave Pomona CA 91768 USA

Volume 8, issue 3 (2008)