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The world problem: on the computability of the topology of 4-manifolds

James R. van Meter
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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.

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James R. van Meter. 2005-06-03. The world problem: on the computability of the topology of 4-manifolds. https://arxiv.org/abs/gr-qc/0506019

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