On 3-manifolds having surface-bundles as branched coverings. (English) Zbl 0631.57003

Montesinos, José María

Proc. Am. Math. Soc. 101, 555-558 (1987).

The author proves that for every closed orientable 3-manifold M and every odd integer m, there is a surface bundle N over \(S^ 1\) which is a 2m- fold branched cyclic covering of M; this generalizes a result of the reviewer [Math. Semin. Notes, Kobe Univ. 9, 159-180 (1981; Zbl 0483.57003)]. He also gives a new proof of the result of R. Brooks [J. Reine Angew. Math. 362, 87-101 (1985; Zbl 0565.57006)] that N can be made hyperbolic in case \(m=1\).

Reviewer: M.Sakuma

MSC:

57M12	Low-dimensional topology of special (e.g., branched) coverings
57N10	Topology of general \(3\)-manifolds (MSC2010)
57M25	Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

open-book; hyperbolic manifold; surface bundle over \(S^ 1\); closed orientable 3-manifold; 2m-fold branched cyclic covering

Citations:

Zbl 0631.57002; Zbl 0483.57003; Zbl 0565.57006