Quasi-isometries of (Z)n and twisted conjugacy in certain linear groups[HBNI Th185]

Abstract

This thesis addresses two problems, which are independent of each other. In the first part, we study QI(Z n ), the quasi-isometry group of the finitely generated abelian group Z n for n ≥ 2. We show that certain groups of diffeomorphisms embed into it and therefore, conclude that QI(Z n ) is “large”. See 2.

In the second part, which is the major part of the thesis, we study twisted conjugacy in general and special linear groups G over polynomial and Laurent polynomial rings over subfields of the algebraic closure of finite fields. See 3.