Consider a map between two complex analytic varieties of finite type $f:X\to Y$. Suppose that $f$ induces isomorphisms on cohomology with (constant) integral coefficients. Under what reasonable hypotheses can we conclude that it induces an equivalence on homotopy groups?

I refer in particular to this article https://arxiv.org/pdf/1710.05366.pdf, Proof of proposition 3.17 on page 14, where the Authors use a result of this kind. I cannot understand why classical hypotheses like nilpotency of the spaces are verified.

Thank you in advance.

  • $\begingroup$ I don't think that the proof you cite can be considered complete. There is no obvious reason why homology equivalence should be sufficient in that context. $\endgroup$ – Neil Strickland Mar 13 at 19:27

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