Milnor's finite generation conjecture for fundamental groups of RCD spaces

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Let (X,d,m)(X,d,\mathfrak{m}) be an RCD∗(0,N)RCD^{\ast}(0,N) space, where RCD∗(0,N)RCD^{\ast}(0,N) denotes the relevant synthetic non-negative Ricci-curvature condition. Milnor's conjecture. The fundamental group π1(X)\pi_1(X) is finitely generated. This asks whether finite generation, known in several settings for spaces of non-negative Ricci curvature, holds for all RCD∗(0,N)RCD^{\ast}(0,N) spaces.

References

Primary source

Jaime Santos-Rodriguez and Sergio Zamora, “On fundamental groups of RCD spaces”, arXiv:2210.07275 (2023).

Additional references

7 papers in this index state this conjecture (2006–2022). The statement above is taken from the most recent of them; the others are arXiv:2006.00745, arXiv:1905.13366, arXiv:1808.02329, arXiv:1108.1888, arXiv:0901.4019, arXiv:math/0612107.

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