An explicit KO-degree map and applications

The goal of this note is to study the analog in unstable ${{\mathbb A}^1}$-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 $K^{MW}_i(F) = GW^i_i(F)$ for $i \leq 3$, which can be thought of as an extension of Matsumoto's celebrated theorem describing $K_2$ of a field. These results provide the first step in a program aimed at computing the sheaf $\pi_{n}^{{\mathbb A}^1}({\mathbb A}^n \setminus 0)$ for $n \geq 4$.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

Self-Enforcing Labour Contracts and Macroeconomic Dynamics

To properly account for the dynamics of the key macroeconomic variables, researchers incorporate various internal propagation mechanisms in their models. In general, these mechanisms implicitly rely on the assumption of a perfect equality between the real wage and the marginal product of labour. This paper features a micro-founded model of a limited-commitment firm, and derive endogenous dynamic labour contracts that produce a different linkage between the real wage and the marginal product of labour. The risk-sharing between the entrepreneur and the worker, both faced with enforcement problems, provides a different type of propagation mechanism. I investigate the dynamic properties of this endogenous rigidity in relation to the initial bargaining power of each agent. Copyright International Atlantic Economic Society 2007internal propagation mechanisms, real business cycle, risk-sharing hypothesis, E12, E49, J30, J31, J41,

Fuzzy Extensions of Databases

International audienc