Heegaard Floer homology and fibred 3-manifolds

Creators: Ni, Yi

Abstract

Given a closed 3 -manifold Y, we show that the Heegaard Floer homology determines whether Y fibres over the circle with a fibre of negative Euler characteristic. This is an analogue of an earlier result about knots proved by Ghiggini and the author.

Additional Information

© 2009 The Johns Hopkins University Press. Manuscript received July 13, 2007; revised October 3, 2008. Dedicated to the memory of Xiao-Song Lin. Research supported in part by a Graduate School Centennial Fellowship at Princeton University, an AIM Five-Year Fellowship, and NSF grant DMS-0805807. The author wishes to thank Paolo Ghiggini, whose work [4] has a great influence on this one. He also wishes to thank David Gabai, Feng Luo, Peter Ozsváth, Jacob Rasmussen and Zoltán Szabó for their encouragement during the course of this work. Special thanks are due to Yinghua Ai for a conversation during which the author realized a gap in an earlier version of this paper, and for helpful discussions on twisted Heegaard Floer homology. He is also grateful to the referee for pointing out a mistake and for providing many constructive suggestions. The earlier versions of this paper were written when the author was at Princeton University and Columbia University.

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