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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
DOI: https://doi.org/10.1090/S0002-9947-1992-1062195-9
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1062195-9
Keywords: Connected sum, Heegaard splitting, maximal triad, prime decomposition, stable equivalence, surface
Article copyright: © Copyright 1992 American Mathematical Society

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