The goal of this note is to study the analog in unstable A1-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 KiMW(F)=GWii(F) for i≤3,
which can be thought of as an extension of Matsumoto's celebrated theorem
describing K2 of a field. These results provide the first step in a program
aimed at computing the sheaf πnA1(An∖0) for n≥4.Comment: 36 Pages, Final version, to appear Journal of Topolog