Journal article
Universal lattices and Property $τ$
- Abstract:
-
We prove that the universal lattices -- the groups $G=\SL_d(R)$ where $R=\Z[x_1,...,x_k]$, have property $\tau$ for $d\geq 3$. This provides the first example of linear groups with $\tau$ which do not come from arithmetic groups. We also give a lower bound for the expanding constant with respect to the natural generating set of $G$. Our methods are based on bounded elementary generation of the finite congruence images of $G$, a generalization of a result by Dennis and Stein on $K_2$ of some f...
Expand abstract
- Publication status:
- Published
Actions
Authors
Bibliographic Details
- Journal:
- INVENTIONES MATHEMATICAE
- Volume:
- 165
- Issue:
- 1
- Pages:
- 209-224
- Publication date:
- 2006-07-01
- DOI:
- EISSN:
-
1432-1297
- ISSN:
-
0020-9910
- Source identifiers:
-
354362
Item Description
- Keywords:
- Pubs id:
-
pubs:354362
- UUID:
-
uuid:ee5d1a9e-d966-495c-9f98-e41f5977e5cc
- Local pid:
- pubs:354362
- Deposit date:
- 2013-11-16
Terms of use
- Copyright date:
- 2006
- Notes:
- 16 pages
If you are the owner of this record, you can report an update to it here: Report update to this record