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

Motto, Michael

doi:10.1090/S0002-9947-1992-1062195-9

Maximal triads and prime decompositions of surfaces embedded in $3$-manifolds
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Trans. Amer. Math. Soc. 331 (1992), 851-867 Request permission

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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Surfaces in three-manifolds and three-manifold triads

Zur dreidimensionalen Topologie

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Les bisections expliquent le théorème de Reidemeister-Singer

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