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BLOBS AND FLIPS ON GEMS

    https://doi.org/10.1142/S0218216506004907Cited by:7 (Source: Crossref)

    In this paper we prove that two n-gems induce the same manifold if and only if they are linked by a finite sequence of gem moves. A gem move is either a blob move, consisting in the creation or cancellation of an n-dipole, or a clean flip, which is a switch of a pair of edges of the same color that thickens an h-dipole, 1 ≤ h ≤ n - 1, or the inverse operation, which slims an h-dipole, 2 ≤ h ≤ n. Moreover we prove that we can reorder the gem moves, so that all the blob creations precede all clean flips which then precede all the blob cancellations. This reordering is of interest because it is an easy matter to decide whether two gems are linked by a finite sequence of clean flips. As a consequence, if a bound for the number of blob creations is established, then there exists a deterministic finite algorithm to decide whether two gems induce the same manifold or not.

    AMSC: Primary 57Q05, Primary 57M15, Secondary 57M12, Secondary 57M25, Secondary 05C10

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