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20.63 (2022)

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a) Prove that every unitarisable group has trivial cost.

b) At least prove that every unitarisable group has vanishing first $L^2$ Betti number.

Contributor: N. Monod

Progress

a) This is known to be true for residually finite groups (I. Epstein, N. Monod, Int. Math. Res. Notes, 2009, no. 22 (2009), 4336–4353).

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