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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

Alternate Heegaard genus bounds distance

Martin Scharlemann and Maggy Tomova

Geometry & Topology 10 (2006) 593–617

DOI: 10.2140/gt.2006.10.593

arXiv: math.GT/0501140

Abstract

Suppose M is a compact orientable irreducible 3–manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized or boundary-stabilized copy of P or the distance d(P) ≤ 2 genus(Q).

More generally, if P and Q are bicompressible but weakly incompressible connected closed separating surfaces in M then either

  • P and Q can be well-separated or

  • P and Q are isotopic or

  • d(P) ≤ 2 genus(Q).

Keywords

Heegaard splitting, Heegaard distance, strongly irreducible, handlebody, weakly incompressible

Mathematical Subject Classification

Primary: 57N10

Secondary: 57M50

References
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Publication

Received: 1 June 2005
Accepted: 27 March 2006
Published: 4 May 2006
Proposed: David Gabai
Seconded: Joan Birman, Cameron Gordon

Authors
Martin Scharlemann
Mathematics Department
University of California
Santa Barbara, CA 93106
USA
Maggy Tomova
Mathematics Department
University of Iowa
Iowa City, IA 52242
USA