The Unsolvability of the Homeomorphism Problem
Stefan Friedl, Tobias Hirsch, Marc Kegel
TL;DR
This paper provides a detailed proof of Markov's theorem demonstrating that the homeomorphism problem is unsolvable and shows that unrecognizable manifolds exist in all dimensions greater than 3.
Contribution
It offers a comprehensive proof of the unsolvability of the homeomorphism problem and establishes the existence of unrecognizable manifolds in higher dimensions.
Findings
Homeomorphism problem is undecidable in all dimensions > 3
Existence of unrecognizable manifolds in higher dimensions
Detailed exposition of Markov's theorem
Abstract
In this short expository note, we give a detailed proof of Markov's theorem on the unsolvability of the homeomorphism problem and of the existence of unrecognizable manifolds in all dimensions larger than 3.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Markov Chains and Monte Carlo Methods