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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Prime $ 3$-manifolds and the doubling operation


Author: Jonathan L. Gross
Journal: Proc. Amer. Math. Soc. 27 (1971), 375-380
MSC: Primary 57.01
DOI: https://doi.org/10.1090/S0002-9939-1971-0271948-8
MathSciNet review: 0271948
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Abstract: Examples are given to show that, in general, one may not factor a compact $ 3$-manifold $ M$ with nonvacuous boundary into primes relative to the multi-disk sum (a boundary pasting operation) by factoring the double of $ M$ into primes relative to the connected sum. Necessary and sufficient conditions for the double of a compact $ 3$-manifold with nonvacuous boundary to be prime relative to the connected sum are established.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0271948-8
Keywords: Connected sum, pasting, irreducible
Article copyright: © Copyright 1971 American Mathematical Society