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On pseudo-Anosov maps which extend over two handlebodies

Published online by Cambridge University Press:  20 January 2009

D. D. Long
D. D. Long
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA. 93106, USA
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Abstract

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We show that there is a pair of handlebodies H1 and H2 with common boundary F with the properties:

(a) There is no essential simple closed curve in F bounding a disc in both H1 and H2.

(b) Given any positive number, there are essential simple curves Cii = 1, 2 on F, bounding discs in Hi whose distance apart in the Hausdorff topology on F is less than this positive number.

Such an example has consequences for Heegaard splittings and recognising the 3-sphere.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 2 , June 1990 , pp. 181 - 190
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

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