Abstract
Let K be a 1-dimensional complex, in a PL 3-manifold M, and let N be a regular neighborhood of K. Then for each edge σ1 of K there is a 2-cell D, “orthogonal to σ1 at the mid-point P of σ1”; D ∩ K = {P}; and the 2-cells D decompose N into a collection of polyhedral 3-cells Cυ, each of which contains exactly one vertex υ of K. The sets C υ will be called the dual cells of N. If K is appropriately subdivided, then the edges σ1 can be made of arbitrarily small diameter, and the neighborhood N can thus be chosen so that the sets C υ are of arbitrary small diameter. The 2-cells D will be called splitting disks of N.
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© 1977 Springer Science+Business Media New York
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Moise, E.E. (1977). Handle decompositions of tubes. In: Geometric Topology in Dimensions 2 and 3. Graduate Texts in Mathematics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9906-6_33
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DOI: https://doi.org/10.1007/978-1-4612-9906-6_33
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