The Unsolvability of the Homeomorphism Problem

📅 2026-03-24
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📝 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.
Problem

Research questions and friction points this paper is trying to address.

homeomorphism problem
unsolvability
unrecognizable manifolds
Markov's theorem
Innovation

Methods, ideas, or system contributions that make the work stand out.

unsolvability
homeomorphism problem
unrecognizable manifolds
Markov's theorem
computational topology
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Stefan Friedl
Stefan Friedl
University of Regensburg
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