A necessary and sufficient condition for a -manifold to have Heegaard genus one

Authors:
Joel Hass and Abigail Thompson

Journal:
Proc. Amer. Math. Soc. **107** (1989), 1107-1110

MSC:
Primary 57N10

MathSciNet review:
984792

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Abstract: Let be a closed -manifold. R. H. Bing showed that is homeomorphic to if and only if every simple closed curve in can be isotoped to lie inside a -ball. We generalize this to show that there is a solid torus imbedded in such that every simple closed curve in can be isotoped to lie in if and only if has a genus one Heegaard splitting.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1989-0984792-4

Article copyright:
© Copyright 1989
American Mathematical Society