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arXiv 2302.014812023-02math.GRmath.GTmath.LO

流形同胚群的一阶刚性

First order rigidity of homeomorphism groups of manifolds

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

备注：: 60 pages. To appear in Communications of the AMS

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AI总结：

本文证明对每个紧致连通流形M，存在群语言中的一阶语句ϕ_M，使得另一紧致流形N的同胚群满足ϕ_M当且仅当N同胚于M，并将该结果推广到保持Oxtoby--Ulam概率测度的同胚群。

摘要：

对于每一个紧致连通流形 $M$，我们证明在群语言中存在一个语句 $ϕ_M$，使得另一个紧致流形 $N$ 的同胚群满足 $ϕ_M$ 当且仅当 $N$ 同胚于 $M$。我们证明了对于保持 Oxtoby--Ulam 概率测度的同胚群的类似陈述。

英文摘要：

For every compact, connected manifold $M$, we prove the existence of a sentence $ϕ_M$ in the language of groups such that the homeomorphism group of another compact manifold $N$ satisfies $ϕ_M$ 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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