RIMS, Kyoto University, 606-8502, Japan (firstname.lastname@example.org)
It is well known that a finitely generated grouphas Kazhdan’s property (T) if and only if the Laplacian element in has a spectral gap. In this paper, we prove that this phenomenon is witnessed in . Namely, has property (T) if and only if there exist a constant and a finite sequence in such that . This result suggests the possibility of finding new examples of property (T) groups by solving equations in , possibly with the assistance of computers.
(Received January 08 2014)
(Revised July 18 2014)
(Accepted July 18 2014)
2010 Mathematics subject classification:
The author was partially supported by JSPS (23540233).