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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.

References [Enhancements On Off] (What's this?)

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Keywords: 3-manifold, irreducible, prime, covering space, incompressible, 2-sided projective plane, cube-with-a-knotted-hole
Article copyright: © Copyright 1972 American Mathematical Society

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