arXiv:gr-qc/0506019gr-qc
The world problem: on the computability of the topology of 4-manifolds
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Abstract
Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing machine with an arbitrary input can be encoded into the topology of a 4-manifold, such that the 4-manifold is homeomorphic to a certain other 4-manifold if and only if the corresponding Turing machine halts on the associated input. Physical implications are briefly discussed.
If what is suspected is true, then yes, strong Church-Turing is false. If there's a symmetry in QCD that makes simulation possible in polynomial time, i.e. a helpful property that is true of QCD specifically but absent from the more general class of integrals its solutions…
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