ETALE HOMOTOPY AND SUMS-OF-SQUARES FORMULAS (2009)
Abstract. This paper uses a relative of BP-cohomology to prove a theorem in characteristic p algebra. Specifically, we obtain some new necessary conditions for the existence of sums-of-squares...
EIGENTHEORY OF CAYLEY-DICKSON ALGEBRAS (2009)
Daniel K. Biss, J. Daniel Christensen, Daniel Dugger, C. Isaksen
Abstract. We show how eigentheory clarifies many algebraic properties of Cayley-Dickson algebras. These notes are intended as background material for those who are studying this eigentheory more...
Large annihilators in Cayley-Dickson algebras (2009)
Daniel K. Biss, J. Daniel Christensen, Daniel Dugger, C. Isaksen
Abstract. We establish many previously unknown properties of zero-divisors in Cayley-Dickson algebras. The basic approach is to use a certain splitting that simplifies computations surprisingly. 1.
Large annihilators in Cayley-Dickson algebras (2008)
Daniel K. Biss, Daniel Dugger, C. Isaksen
Abstract. Cayley-Dickson algebras are non-associative R-algebras that generalize the well-known algebras R, C, H, and O. We study zero-divisors in these algebras. In particular, we show that the...
Obstruction theory in model categories (2008)
J. Daniel Christensen, William G. Dwyer, C. Isaksen
Abstract. Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite...
Obstruction theory in model categories (2007)
J. Daniel Christensen, William G. Dwyer, C. Isaksen
Abstract. Working in an arbitrary pointed proper model category, we describe the cobrations that have an obstruction theory with respect to all brations. Up to weak equivalence, retract, and cobase...