Proceedings of the American Mathematical Society

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



A sufficient condition for surfaces in $ 3$-manifolds to have unique prime decompositions

Author: Michael Motto
Journal: Proc. Amer. Math. Soc. 120 (1994), 1275-1280
MSC: Primary 57N10; Secondary 57M99, 57Q35
MathSciNet review: 1195727
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Abstract: In 1975, Suzuki proved that prime decompositions of closed, connected surfaces in $ {S^3}$ are unique up to ambient isotopy if the surface bounds a $ 3$-manifold whose factors under the prime decomposition all have incompressible boundary. This paper extends this result to surfaces in more general $ 3$-manifolds, when there is a prime decomposition for which every factor of the surface is incompressible on one side.

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Keywords: Heegaard splitting, prime decomposition, surface
Article copyright: © Copyright 1994 American Mathematical Society