Destabilizing amalgamated Heegaard splittings

Details Destabilizing amalgamated Heegaard splittings Destabilizing amalgamated Heegaard splittings

2005-10-18

arxiv.org/abs/math/0510386v2

Geom. Topol. Monogr. 12 (2007) 319-334

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 3 December 2007

Scientific paper

10.2140/gtm.2007.12.319

We construct a sequence of pairs of 3-manifolds each with torus boundary and with the following two properties: 1) For the result of a carefully chosen glueing of the nth pair of 3-manifolds along their boundary tori, the ratio of the genus of the resulting 3-manifold to the sum of the genera of the pair of 3-manifolds is less than 1/2. 2) The result of amalgamating certain unstabilized Heegaard splittings of the pair of 3-manifolds to form a Heegaard splitting of the resulting 3-manifold produces a stabilized Heegaard splitting that can be destabilized successively n times.

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