Unrecognizability of manifolds

Annals of Pure and Applied Logic 141 (3):325-335 (2006)

We present a modernized proof, with a modification by M.A. Shtan’ko, of the Markov theorem on the unsolvability of the homeomorphy problem for manifolds. We then discuss a proof of the S.P. Novikov theorem on the unrecognizability of spheres for n≥5, from which we obtain a corollary about unrecognizability of all manifolds of dimension at least five. An analogous argument then proves the unrecognizability of stabilizations of all four-dimensional manifolds. We also give a brief overview of known results concerning algorithmic recognizability of three-dimensional manifolds
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DOI 10.1016/j.apal.2005.12.011
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References found in this work BETA

Recursive Unsolvability of Group Theoretic Problems.Michael O. Rabin - 1958 - Journal of Symbolic Logic 23 (1):55-56.

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Finite Axiomatizability in Łukasiewicz Logic.Daniele Mundici - 2011 - Annals of Pure and Applied Logic 162 (12):1035-1047.

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