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

paniniv@gmail.com, Charles.Walter@unice.fr

Submission: 2010, Nov 2

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.

2000 Mathematics Subject Classification: 14F42, 19G38, 19E20, 19E08

Keywords and Phrases: Hermitian K-theory, algebraic symplectic cobordism, Pontryagin classes, Thom classes, change of coefficients.

Full text: dvi.gz 33 k, dvi 99 k, ps.gz 958 k, pdf.gz 167 k, pdf 280 k.

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