On the Construction of Branched Coverings of Low-Dimensional Manifolds
Open Access
- 1 January 1979
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 247, 87-124
- https://doi.org/10.2307/1998776
Abstract
Several general results are proved concerning the existence and uniqueness of various branched coverings of manifolds in dimensions 2 and 3. The results are applied to give a rather complete account as to which 3-manifolds are branched coverings of , , , or the nontrivial -bundle over , and which degrees can be achieved in each case. In particular, it is shown that any closed nonorientable 3-manifold is a branched covering of of degree which can be chosen to be at most 6 and with branch set a simple closed curve. This result is applied to show that a closed nonorientable 3-manifold admits an open book decomposition which is induced from such a decomposition of .Keywords
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