Volume 14 (2008)

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ISSN (electronic): 1464-8997
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Refilling meridians in a genus 2 handlebody complement

Martin Scharlemann

Geometry & Topology Monographs 14 (2008) 451–475

DOI: 10.2140/gtm.2008.14.451

arXiv: math/0603705

Abstract
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Suppose a genus two handlebody is removed from a 3–manifold M and then a single meridian of the handlebody is restored. The result is a knot or link complement in M and it is natural to ask whether geometric properties of the link complement say something about the meridian that was restored. Here we consider what the relation must be between two not necessarily disjoint meridians so that restoring each of them gives a trivial knot or a split link.

Dedicated to the memory of Heiner Zieschang, first to notice that genus two handlebodies could be interesting

Keywords

Mathematical Subject Classification

Primary: 57N10

Secondary: 57M50

References
Publication

Received: 30 March 2006
Revised: 26 April 2007
Accepted: 26 April 2007
Published: 29 April 2008

Authors
Martin Scharlemann
Mathematics Department
University of California
Santa Barbara, CA USA