### On the relation of symplectic algebraic cobordism to hermitian K-theory, by Ivan Panin and Charles Walter

We reconstruct hermitian K-theory via algebraic symplectic cobordism. In the
motivic stable homotopy category SH(S) there is a unique morphism g : MSp -> BO
of commutative ring T- spectra which sends the Thom class th^{MSp} to the Thom
class th^{BO}. We show that the induced morphism of bigraded cohomology
theories MSp^{*,*} -> BO^{*,*} is isomorphic to the morphism of bigraded
cohomology theories obtained by applying to MSp^{*,*} the ``change of (simply
graded) coefficients rings'' MSp^{4*,2*} -> BO^{4*,2*}. This is an algebraic
version of the theorem of Conner and Floyd reconstructing real K-theory via
symplectic cobordism.

Ivan Panin <paniniv@gmail.com>

Charles Walter <Charles.Walter@unice.fr>