Algebraic K-theory and sums-of-squares formulas

Daniel Dugger and Daniel C. Isaksen

Email: ddugger@math.uoregon.edu and isaksen@math.wayne.edu

Addresses:

Daniel Dugger
Department of Mathematics
University of Oregon
Eugene, OR 97403

Daniel C. Isaksen
Department of Mathematics
Wayne State University
Detroit, MI 48202

Abstract:

We prove a result about the non-existence of certain sums-of-squares
formulas over a field.  This generalizes an old theorem which used
topological K-theory to produce obstruction conditions when the field
is the real numbers.  Our result applies to arbitrary fields not of
characteristic 2, making use of algebraic K-theory in place of
topological K-theory.