Destabilizing amalgamated Heegaard splittings

Jennifer Schultens; Richard Weidmann

doi:10.2140/gtm.2007.12.319

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Destabilizing amalgamated Heegaard splittings

Jennifer Schultens·Richard Weidmann

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Abstract

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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BibTeX RIS

Jennifer Schultens, Richard Weidmann. 2009-04-01. Destabilizing amalgamated Heegaard splittings. https://doi.org/10.2140/gtm.2007.12.319

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