Volume 14 (2008)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
 
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN 1464-8997 (online)
ISSN 1464-8989 (print)
 
MSP Books and Monographs
Other MSP Publications

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

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