Volume 10, issue 4 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Heegaard splittings with large subsurface distances

Jesse Johnson, Yair Minsky and Yoav Moriah

Algebraic & Geometric Topology 10 (2010) 2251–2275
Abstract

We show that subsurfaces of a Heegaard surface for which the relative Hempel distance of the splitting is sufficiently high have to appear in any Heegaard surface of genus bounded by half that distance.

Keywords
Heegaard splitting, curve complex, subsurface projection
Mathematical Subject Classification 2000
Primary: 57M99
Secondary: 57R99
References
Publication
Received: 25 February 2010
Revised: 26 July 2010
Accepted: 27 August 2010
Published: 23 November 2010
Authors
Jesse Johnson
Department of Mathematics
Oklahoma State University
401 MSCS
Stillwater OK 74078
USA
http://www.math.okstate.edu/~jjohnson/
Yair Minsky
Department of Mathematics
Yale University
10 Hillhouse Ave
New Haven CT 06520-8283
USA
http://www.math.yale.edu/users/yair
Yoav Moriah
Department of Mathematics
Technion
32000 Haifa
Israel
http://www.math.technion.ac.il/~ymoriah/