First order rigidity of homeomorphism groups of manifolds

First order rigidity of homeomorphism groups of manifolds

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 homeomorph...

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Hauptverfasser: Kim, Sang-hyun, Koberda, Thomas, González, J. de la Nuez
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Geometric Topology
Mathematics - Group Theory
Mathematics - Logic
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Zusammenfassung: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.
DOI:10.48550/arxiv.2302.01481