The Domino Problem of the Hyperbolic Plane Is Undecidable

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Margenstern, Maurice
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Abstract
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In this paper, we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is undecidable for the Euclidean plane, initially proved by Robert Berger in 1966.
Comment: 18 pages, This is a synthesis of previous deposits
Keywords
Computer Science - Computational Geometry, Computer Science - Discrete Mathematics, F.2.2
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