On non-compact Heegaard splittings

Scott Taylor

doi:10.2140/agt.2007.7.603

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On non-compact Heegaard splittings

Scott Taylor

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Abstract

A Heegaard splitting of an open 3-manifold is the partition of the manifold into two non-compact handlebodies which intersect on their common boundary. This paper proves several non-compact analogues of theorems about compact Heegaard splittings. The main theorem is: if N is a compact, connected, orientable 3-manifold with non-empty boundary, containing no S^2 components, and if M is obtained from N by removing the boundary then any two Heegaard splittings of M are properly ambient isotopic. This is a non-compact analogue of the classifications of splittings of (closed surface) x I and (closed surface) x S^1 by Scharlemann-Thompson and Schultens. Work of Frohman-Meeks and a non-compact analogue of the Casson-Gordon theorem on weakly reducible Heegaard splittings are key tools.

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BibTeX RIS

Scott Taylor. 2006-04-11. On non-compact Heegaard splittings. https://doi.org/10.2140/agt.2007.7.603

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