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Published August 2009 | Submitted
Journal Article Open

Dehn surgeries that yield fibred 3-manifolds

Ni, Yi

Abstract

We study Dehn surgeries on null-homotopic knots that yield fibred 3-manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai's theory of sutured manifold decomposition. Such surgeries are negative examples to a question of Michel Boileau. Another result we will prove is about surgeries which reduce the Thurston norm of a fibred manifold.

Additional Information

© 2009 Springer. Received: 28 December 2007 / Revised: 20 October 2008 / Published online: 10 January 2009. We are grateful to Michel Boileau, David Gabai and Tao Li for some very interesting discussions, to Marc Lackenby for helpful comments, and to John Luecke for a detailed description of his earlier proof of a special case of Theorem 1.4. The author is partially supported by an AIM Five-Year Fellowship. This research was partially conducted during the period the author was employed by the Clay Mathematics Institute as a Liftoff Fellow, and when the author visited University of Minnesota, Twin Cities. The author wishes to thank the above institutions for their supports, and special thanks are due to Tian-Jun Li for his hospitality.

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August 20, 2023
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