Volume 14, issue 4 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Heegaard surfaces and the distance of amalgamation

Tao Li

Geometry & Topology 14 (2010) 1871–1919
Abstract

Let M1 and M2 be orientable irreducible 3–manifolds with connected boundary and suppose M1M2. Let M be a closed 3–manifold obtained by gluing M1 to M2 along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then M is not homeomorphic to S3 and all small-genus Heegaard splittings of M are standard in a certain sense. In particular, g(M) = g(M1) + g(M2) g(Mi), where g(M) denotes the Heegaard genus of M. This theorem is also true for certain manifolds with multiple boundary components.

Keywords
Heegaard splitting, amalgamation, curve complex
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M50
References
Publication
Received: 31 July 2008
Revised: 9 March 2010
Accepted: 7 June 2010
Published: 21 July 2010
Proposed: Cameron Gordon
Seconded: Joan Birman, Colin Rourke
Authors
Tao Li
Department of Mathematics
Boston College
Chestnut Hill, MA 02467
http://www2.bc.edu/~taoli/