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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Irreducible $ 3$-manifolds whose orientable covers are not prime


Author: W. H. Row
Journal: Proc. Amer. Math. Soc. 34 (1972), 541-545
MSC: Primary 57A10
MathSciNet review: 0296947
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Abstract: J. L. Tollefson has asked if every closed covering space of a prime 3-manifold is prime. In the present paper, the author provides a negative answer by constructing infinitely many topologically distinct, irreducible, closed 3-manifolds with the property that none of their orientable covering spaces are prime. These 3-manifolds are distinguished by the maximum number of disjoint, nonparallel, 2-sided projective planes that they contain. The author does not know if every closed covering space of a prime, orientable 3-manifold is prime.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0296947-2
PII: S 0002-9939(1972)0296947-2
Keywords: 3-manifold, irreducible, prime, covering space, incompressible, 2-sided projective plane, cube-with-a-knotted-hole
Article copyright: © Copyright 1972 American Mathematical Society