Positive synthetic Ricci curvature conjecture for orientable Alexandrov spaces

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Let MM be an orientable Alexandrov space of dimension nn without boundary. Assume that a synthetic lower Ricci curvature bound, in the terminology of optimal transport theory, is nonnegative everywhere and positive at at least one point.

Positive synthetic Ricci curvature conjecture. Under these assumptions,

Hn−1(M;R)=0.H_{n-1}(M;\mathbb R)=0.

This would extend the vanishing result proved in the paper for spaces satisfying a stronger positive curvature-dimension condition. The supplied source does not state that the conjecture has been proved or disproved.

References

Primary source

Ayato Mitsuishi, “Orientability and fundamental classes of Alexandrov spaces with applications”, arXiv:1610.08024 (2016).

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