Irreducible 3-manifolds whose orientable covers are not prime

Row, W. H.

doi:10.1090/S0002-9939-1972-0296947-2

Irreducible $3$-manifolds whose orientable covers are not prime
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by W. H. Row PDF

Proc. Amer. Math. Soc. 34 (1972), 541-545 Request permission

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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