Year: 1996
Type: article
Abstract: In [FS], B. Farb and I emended the techniques of [Sch] to prove that (1", H 2 • H 2) is quasi-isometrically rigid provided that 1" is non-uniform and irreducible.Such lattices are all arithmetic, and as a corollary, we obtain the same result as above for real quadratic fields. Statement of resultsA number field is a finite-degree field extension of Q.To save words, we will always take non-trivial extensions of Q.Given such a number field, K, with corresponding ring (_0 of algebraic integers, the finitely generated group PSL2(O) is an irredicible lattice in Is(XK).Here XK is a product of two-and three-dimensional hyperbolic spaces.Comm(PSL2(O), XK) contains PGL2(K) as a normal subgroup of finite index.
Source: Acta Mathematica
DOI: 10.1007/bf02392599
Author: Richard Evan Schwartz
Institution: University of Maryland, College Park
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2040103482