55
votes
How feasible is it to prove Kazhdan's property (T) by a computer?
I think it is appropriate to let MO users know (the OP himself knows it well) that this question was recently solved: it is feasible to provide a computer based proof for property (T) using the Ozawa ...
- 11.6k
13
votes
Is there a one relator group with property (T)?
In fact, much more is true: if $H$ is a finitely generated subgroup of a one-relator group and $H$ has property (T) then $H$ is finite. Indeed, a classical theorem of Brodskii and Howie asserts that ...
- 25.2k
8
votes
Properties (T) and (FA)
Here is a point of view which justifies why Property $(FA)$ is a very particular case of Property $(T)$. First, Chatterji-Drutu-Haglund proved that:
Theorem: A discrete group has $(T)$ iff all its ...
- 8,401
8
votes
Accepted
Kazhdan's property (T) for $\tilde{C}_2$-lattices
I don't have access to Zuk's note, but I remember finding an error in it when I read it (so this could be the same problem you found). He did improve on Garland in terms of thickness by taking average ...
- 1,163
6
votes
Is there a one relator group with property (T)?
Property (T) implies Property FA: every action on a tree has a global fixpoint. The Magnus–Moldavanskii hierarchy expresses every one-relator group as (a subgroup of) an HNN extension of a "...
- 3,736
4
votes
Accepted
Residual finiteness of random groups with property (T)
This is an open question: there are no densities $1/2>d\geq 1/6$ where a random group is known to be residually finite. Any progress would be a major step forward.
As mentioned in the question, at ...
- 25.2k
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