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Questions about the branch of algebra that deals with groups.

7 votes
1 answer
141 views

Discrete cocompact group of isometries of Nil

Is it true that every group quasi-isometric to the Heisenberg group admits a proper cocompact action by isometries on Nil?
George K's user avatar
  • 422
7 votes
3 answers
1k views

Bass-Serre theory textbook

I am a PhD freshman working on topological graph theory and geometric group theory. I would like to learn some Bass-Serre theory. What do you think is the best introductory textbook in this topic? Tha …
George K's user avatar
  • 422
5 votes
1 answer
92 views

Infinite groups that admit a discrete, co-compact, bilipschitz action on $\mathbb{R}^3$

Apart from the abstract types of the crystallographic groups, are there any other abstract groups that admit a proper, co-compact, uniformly bilipschitz action on $\mathbb{R}^3$?
George K's user avatar
  • 422