13 research outputs found
An explicit KO-degree map and applications
The goal of this note is to study the analog in unstable -homotopy theory of the unit map from the motivic sphere spectrum to the
Hermitian K-theory spectrum, i.e., the degree map in Hermitian K-theory. We
show that "Suslin matrices", which are explicit maps from odd dimensional split
smooth affine quadrics to geometric models of the spaces appearing in Bott
periodicity in Hermitian K-theory, stabilize in a suitable sense to the unit
map. As applications, we deduce that for ,
which can be thought of as an extension of Matsumoto's celebrated theorem
describing of a field. These results provide the first step in a program
aimed at computing the sheaf for .Comment: 36 Pages, Final version, to appear Journal of Topolog
A coproduct structure on the formal affine Demazure algebra
In the present paper we generalize the coproduct structure on nil Hecke rings
introduced and studied by Kostant-Kumar to the context of an arbitrary
algebraic oriented cohomology theory and its associated formal group law. We
then construct an algebraic model of the T-equivariant oriented cohomology of
the variety of complete flags.Comment: 28 pages; minor revision of the previous versio