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On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces

Published online by Cambridge University Press:  20 November 2018

Masakazu Teragaito
Masakazu Teragaito*
Affiliation:
Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524 e-mail: teragai@hiroshima-u.ac.jp
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Abstract

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For a non-trivial knot in the 3-sphere, only integral Dehn surgery can create a closed 3-manifold containing a projective plane. If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true. In contrast to these, we show that non-integral surgery on a hyperbolic knot can create a closed non-orientable surface of any genus greater than two.

Keywords

57M25knotDehn surgerynon-orientable surface
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 4 , 01 December 2006 , pp. 624 - 627
Copyright
Copyright © Canadian Mathematical Society 2006

References

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