There are well-known results about nilpotent and solvable (=virtually nilpotent) Kähler groups coming from the work of (to name a few) Campana, Carlson-Toledo, Arapura-Nori, Delzant...

  1. Are there any interesting known restrictions on amenable Kähler groups?
  2. What about interesting known examples?

More generally,

Definition. A group $G$ is a von-Neumann group if it does not contain a non-abelian free group.

It is clear that any amenable group is a von-Neumann group.

  1. What is known about Kähler groups which are also von-Neumann group?

1 Answer 1


For 1: beyond the case of nilpotent/solvable groups, I know of no restrictions on amenable kähler groups.

For 3: this is an interesting question but again I know of no restriction. This is probably due to our lack of ideas or to the lack of any suitable technology.

For 2: besides the 2-step nilpotent Kähler groups (not virtually Abelian) built in the 90s (Campana, Carlson-Toledo), I know of no new examples. In particular I think that it is still unknown whether there can be some 3-step nilpotent examples (not virtually 2-step nilpotent).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.