Algebraic KK-theory and sums-of-squares formulas

  • Daniel Dugger

  • Daniel C. Isaksen

    Department of Mathematics Department of Mathematics University of Oregon Wayne State University Eugene, OR 97403, USA Detroit, MI 48202, USA
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We prove a result about the existence of certain 'sums-of-squares' formulas over a field FF. A classical theorem uses topological KK-theory to show that if such a formula exists over R\mathbb R, then certain powers of 2 must divide certain binomial coefficients. In this paper we use algebraic KK-theory to extend the result to all fields not of characteristic 2.

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Daniel Dugger, Daniel C. Isaksen, Algebraic KK-theory and sums-of-squares formulas. Doc. Math. 10 (2005), pp. 357–366

DOI 10.4171/DM/192