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Destabilizing amalgamated Heegaard splittings

Jennifer Schultens and Richard Weidmann

Geometry & Topology Monographs 12 (2007) 319–334

DOI: 10.2140/gtm.2007.12.319

arXiv: math.GT/0510386

Abstract

We construct a sequence of pairs of 3–manifolds (M1n, M2n) each with incompressible torus boundary and with the following two properties:

(1) For Mn the result of a carefully chosen glueing of M1n and M2n along their boundary tori, the genera (g1n, g2n) of (M1n, M2n) and the genus gn of Mn satisfy the inequality
gn/(g1n + g2n) < 1/2.

(2) The result of amalgamating certain unstabilized Heegaard splittings of M1n and M2n to form a Heegaard splitting of M produces a stabilized Heegaard splitting that can be destabilized successively n times.

Keywords

Heegaard genus, 3–manifolds, destabilizations

Mathematical Subject Classification

Primary: 57M27

References
Publication

Received: 20 January 2007
Revised: 12 March 2007
Accepted: 12 March 2007
Published: 3 December 2007

Authors
Jennifer Schultens
Department of Mathematics
University of California, Davis
1 Shields Avenue
Davis CA 95616
USA
Richard Weidmann
Department of Mathematics and Maxwell Institute of Mathematical Sciences
Heriot-Watt University
Riccarton
Edinburgh
EH14 4AS
Scotland