Algorithmic aspects of immersibility and embeddability

12/21/2018

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by   Fedor Manin, et al.

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We analyze an algorithmic question about immersion theory: for which m, n, and CAT=Diff or PL is the question of whether an m-dimensional CAT-manifold is immersible in R^n decidable? As a corollary, we show that the smooth embeddability of an m-manifold with boundary in R^n is undecidable when n-m is even and 11m ≥ 10n+1.