In addition to his seminal work in topology, John Milnor is also an accomplished algebraist, producing a spectacular agenda-setting body of work related to algebraic \(K\)-theory and quadratic forms during the five year period 1965-1970. These papers, together with other (some of them previously unpublished) works in algebra are assembled here in this fifth volume of Milnor's Collected Papers. They constitute not only an important historical archive, but also, thanks to the clarity and elegance of Milnor's mathematical exposition, a valuable resource for work in the fields treated. In addition, Milnor's papers are complemented by detailed surveys on the current state of the field in two areas. One is on the congruence subgroup problem, by Gopal Prasad and Andrei Rapinchuk. The other is on algebraic \(K\)-theory and quadratic forms, by Alexander Merkurjev.

Readership

Graduate students and research mathematicians interested in algebra and group theory.

Reviews

"It is wonderful to see these papers which appear as part of volume 5 of the collected works of John Milnor. Particularly, there are some unpublished papers which were the preliminary versions of some of the author's path-breaking papers. There are also some articles which appeared in conference proceedings and which may not have received as much exposure as one might desire. Milnor's work in the subjects appearing in this volume has given birth to whole programs and set the agenda of research in these subjects for the last five decades. The volume is divided into three parts. . . . [E]ach of the three parts starts with a succinct description of its contents by the editors. . . . [T]his volume is a treasure-house."

-- B. Sury, Mathematical Reviews