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• W2785162637 abstract "We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in R 3 ? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold X into the 3-sphere S 3 . The main step, which allows us to simplify X and recurse, is in proving that if X can be embedded in S 3 , then there is also an embedding in which X has a short meridian , that is, an essential curve in the boundary of X bounding a disk in S 3 X with length bounded by a computable function of the number of tetrahedra of X ." @default.
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• W2785162637 date "2018-01-23" @default.
• W2785162637 modified "2023-09-27" @default.
• W2785162637 title "Embeddability in the 3-Sphere Is Decidable" @default.
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• W2785162637 doi "https://doi.org/10.1145/3078632" @default.
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