On branched coverings of 3-manifolds which fiber over the circle. (English) Zbl 0565.57006

Brooks, Robert

J. Reine Angew. Math. 362, 87-101 (1985).

We show that any 3-manifold has a branched double covering which is hyperbolic and fibers over the circle. The genus of the fiber can be taken to be max(2,H(M)), where H(M) is the Heegaard genus of M.

MSC:

57M12	Low-dimensional topology of special (e.g., branched) coverings
57N10	Topology of general \(3\)-manifolds (MSC2010)

Keywords:

hyperbolic 3-manifold; fibre bundles over the circle; branched double covering; Heegaard genus