BAK’S WORK ON LOWER K-THEORY OF RINGS

Abstract. This paper is a survey of contributions of Anthony Bak to Algebra and (lower) Algebraic K-theory and some of their consequences. We present an overview of his work in these areas, briefly describe the setup and problems as well as the methods introduced by Bak to attack these problems and state some of the crucial theorems. The aim is to analyze in details some of his methods which are quite important and promising for further work in the subject. Among the topics covered are 1) definition of unitary/general quadratic groups over form rings, 2)structure theory and stability for classical groups and their generalisations, 3) quadratic K2 and the quadratic Steinberg groups 4) nilpotent K-theory and localisation-completion 5) Intermediate subgroups 6) congruence subgroup problem, and 7) dimension theory. On the other hand, we do not touch work of Bak pertaining to or motivated by topology, including global actions, surgery theory, transformation groups and smooth actions. On the occasion of his sixtieth birthday, To TONY BAK; with respect and affectio