I don't know how to prove the following observation.
Take $G$ a connected Lie group such that $H^1(G,\mathbb{R})=0$ so the Betti's number is zero and this implies that $H^{1}(G,\mathbb{Z})$ is finite.
Can anyone help me?
thanks in advance
2026-02-23 07:41:22.1771832482
Betti's number and homology with integer coefficients
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