Heegaard gradient and virtual fibers

Maher, Joseph¹

¹ Mathematics 253-37, California Institute of Technology, Pasadena, California 91125, USA

Geometry & topology, Tome 9 (2005) no. 4, pp. 2227-2259.

Résumé

We show that if a closed hyperbolic 3–manifold has infinitely many finite covers of bounded Heegaard genus, then it is virtually fibered. This generalizes a theorem of Lackenby, removing restrictions needed about the regularity of the covers. Furthermore, we can replace the assumption that the covers have bounded Heegaard genus with the weaker hypotheses that the Heegaard splittings for the covers have Heegaard gradient zero, and also bounded width, in the sense of Scharlemann–Thompson thin position for Heegaard splittings.

Détail

DOI : 10.2140/gt.2005.9.2227

Keywords: Heegaard splitting, virtual fiber, hyperbolic $3$–manifold

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