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Journal of Topology 2008 1(2):269-284; doi:10.1112/jtopol/jtn003
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© 2008 London Mathematical Society

Criteria for virtual fibering

Ian Agol

University of California, Berkeley, 970 Evans Hall # 3840, Berkeley, CA 94720-3840, USA ianagol@gmail.com


  Abstract

We prove that an irreducible 3-manifold with fundamental group that satisfies a certain group-theoretic property called RFRS is virtually fibered. As a corollary, we show that 3-dimensional reflection orbifolds and arithmetic hyperbolic orbifolds defined by a quadratic form virtually fiber. These include the Seifert Weber dodecahedral space and the Bianchi groups. Moreover, we show that a taut-sutured compression body has a finite-sheeted cover with a depth one taut-oriented foliation.

Received July 29, 2007.

2000 Mathematics Subject Classification 57M

The author was partially supported by NSF grant DMS-0504975, and the J. S. Guggenheim Foundation.


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