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APPLICATIONS Topology and its Applications 90 (1998) 135-147
 

Summary: ELSEVIER
TOPOLOGY
AND ITS
APPLICATIONS
Topology and its Applications 90 (1998) 135-147
Local detection of strongly irreducible Heegaard splittings
Martin Scharlemann `12
University of California, Department of Mathematics, Sania Barbara, CA 931063080, USA
Received 17 January 1997; received in revised form 30 June 1997
Abstract
Let S be a Heegaard splitting surface of a compact orientable 3-manifold M. If S is strongly
irreducible, the manner in which it can intersect a ball or a solid torus in M is very constrained
and the allowable configurations are simple and useful. Splitting surfaces not conforming to these
simple local pictures must be weakly reducible. 0 1998 Elsevier Science B.V. All rights reserved.
Keywords: Compression body; Heegaard splitting; Strongly irreducible
AMS classijcation: Primary 57N10, Secondary 57M50
0. Introduction
The study of Heegaard splittings of compact orientable 3-manifolds has become dra-
matically more useful since Casson and Gordon introduced the notion of strongly irre-
ducible splittings [2]. All irreducible splittings of non-Haken 3-manifolds are also strongly

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics