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Montesinos Amilibia, José María (1985) Lectures on 3fold simple coverings and 3manifolds. In Combinatorial methods in topology and algebraic geometry. Contemporary Mathematics (44). American Mathematical Society, Providence, pp. 157177. ISBN 0821850393

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Abstract
The author presents various ideas, proofs, constructions and tricks connected with branched coverings of 3manifolds. After an introductory section on 2fold branched coverings of S3 the main theme of 3fold irregular coverings is introduced.
A short proof is given of the MontesinosHilden theorem concerning the presentation of a (closed, oriented) 3manifold as an irregular 3fold covering of S3. Coloured links, associated with irregular 3fold coverings, are discussed, and moves on coloured links which do not alter the associated covering.
The last section contains an elegant proof of a theorem of Hilden and the author: Every closed oriented 3manifold is a simple 3fold covering of S3 branched over a knot so that the branching cover bounds an embedded disc. A consequence of this is the fact that every such 3manifold is parallelizable. Finally the following result of H. M. Hilden , M. T. Lozano and the author [Trans. Amer. Math. Soc. 279 (1983), no. 2, 729–735;] is proved: Every closed oriented 3manifold is the pullback of any 3fold simple branched covering p:S3→S3 and some smooth map Ω:S3→S3 transversal to the branching set of p. This implies an earlier result of Hilden: the possibility to embed any closed oriented 3manifold M in S3×D2 so that the composition with the projection in the first factor is a 3fold simple covering.
Item Type:  Book Section 

Uncontrolled Keywords:  3manifolds as branched coverings of the 3sphere; surfaces as branched covers of S 2 ; Dehn surgery; simple covers; coloured links; Poincaré conjecture; parallelizable 
Subjects:  Sciences > Mathematics > Topology 
ID Code:  22069 
Deposited On:  24 Jun 2013 17:28 
Last Modified:  09 Sep 2020 08:17 
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