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arXiv · 1705.04466

Recognizing the flat torus among $RCD^*(0,N)$ spaces via the study of the first cohomology group

Nicola Gigli·Chiara Rigoni
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Abstract

We prove that if the dimension of the first cohomology group of a $RCD^*(0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences.

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Nicola Gigli, Chiara Rigoni. 2017-05-12. Recognizing the flat torus among $RCD^*(0,N)$ spaces via the study of the first cohomology group. https://arxiv.org/abs/1705.04466

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