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arXiv · 2501.07522

The Lodha--Moore groups and their $n$-adic generalizations are not SCY

Yuya Kodama·Akihiro Takano
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Abstract

A closed 4-manifold is symplectic Calabi--Yau (SCY) if its canonical class is trivial. Friedl and Vidussi proved that Thompson's group $F$ cannot be the fundamental group of any SCY manifold. In this paper, we show that its generalizations, called the Brown--Thompson group and the $n$-adic Lodha--Moore groups, cannot be also the fundamental group of any SCY manifold by using their method. From this proof, we also show that there exist non-trivial infinitely many examples which satisfy Geoghegan's conjecture.

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Yuya Kodama, Akihiro Takano. 2025-01-14. The Lodha--Moore groups and their $n$-adic generalizations are not SCY. https://arxiv.org/abs/2501.07522

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