### The additivity theorem in algebraic K-theory, by Daniel R. Grayson

[ Feb 15 and 21, 2011 : the author has provided an improved version that corrects some
misprints and fixes some garbled quantifiers, replacing the version posted Jan
1, 2011.]

The additivity theorem in algebraic K-theory, due to Quillen and Waldhausen, is
a basic tool. In this paper we present a new proof, which proceeds by
constructing an explicit homotopy combinatorially.

Daniel R. Grayson <dan@math.uiuc.edu>