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arXiv · 2302.01481

First order rigidity of homeomorphism groups of manifolds

Sang-hyun Kim·Thomas Koberda·J. de la Nuez González
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Abstract

For every compact, connected manifold $M$, we prove the existence of a sentence $\phi_M$ in the language of groups such that the homeomorphism group of another compact manifold $N$ satisfies $\phi_M$ if and only if $N$ is homeomorphic to $M$. We prove the analogous statement for groups of homeomorphisms preserving an Oxtoby--Ulam probability measure.

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Sang-hyun Kim, Thomas Koberda, J. de la Nuez González. 2023-02-03. First order rigidity of homeomorphism groups of manifolds. https://arxiv.org/abs/2302.01481

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