### Bak's work on K-theory of rings (with an appendix by Max Karoubi), by R. Hazrat and N. Vavilov

This paper studies the work of Bak in Algebra and (lower) Algebraic K-theory
and some later developments stimulated by them. We present an overview of his
work in these areas, describe the setup and problems as well as the methods he
introduced to attack these problems and state some of the crucial theorems. The
aim is to analyse in detail some of his methods which are important and
promising for further work in the subject. Among the topics covered are,
unitary/general quadratic groups over form rings, structure theory and
stability for such groups, quadratic K_{_2} and the quadratic Steinberg
groups, nonstable K-theory and localisation-completion, intermediate subgroups,
congruence subgroup problem, dimension theory and surgery theory.

The appendix by Max Karoubi states some periodicity theorems and conjectures in
an algebraic context which are related to Bak's work.

R. Hazrat <r.hazrat@qub.ac.uk>

N. Vavilov <nikolai-vavilov@yandex.ru>