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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Maximal triads and prime decompositions of surfaces embedded in $ 3$-manifolds

Author: Michael Motto
Journal: Trans. Amer. Math. Soc. 331 (1992), 851-867
MSC: Primary 57N10
MathSciNet review: 1062195
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Abstract: In 1975, Suzuki proved that prime decompositions of connected surfaces in $ {S^3}$ are unique up to stable equivalence of the factors. This paper extends his result to a large class of $ 3$-manifolds, and demonstrates that this result does not apply to all $ 3$-manifolds. It also answers a question he raised by showing that it is possible for inequivalent surfaces in $ {S^3}$ of the same genus to be stably equivalent. The techniques used involve the notion of Heegaard splittings of $ 3$-manifold triads.

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Keywords: Connected sum, Heegaard splitting, maximal triad, prime decomposition, stable equivalence, surface
Article copyright: © Copyright 1992 American Mathematical Society