On the algebraic cobordism spectra MSL and MSp, by Ivan Panin and Charles Walter

We construct algebraic cobordism spectra MSL and MSp. They are commutative monoids in the category of symmetric T^{2}- spectra. The spectrum MSp comes with a natural symplectic orientation given either by a tautological Thom class th^{MSp} in MSp^{4,2}(MSp_{2}), a tautological Pontryagin class p_{1}^{MSp} in MSp^{4,2}(HP^{\infty}) or any of six other equivalent structures. For a commutative monoid E in the category SH(S) we prove that assignment g -> g(th^{MSp}) identifies the set of homomorphisms of monoids g : MSp -> E in the motivic stable homotopy category SH(S) with the set of tautological Thom elements of symplectic orientations of E. A weaker universality result is obtained for MSL and special linear orientations.

• 0979.bib (254 bytes)
• Panin_Walter_MSp.dvi (313440 bytes) [November 2, 2010]
• Panin_Walter_MSp.dvi.gz (96151 bytes)
• Panin_Walter_MSp.pdf (435633 bytes) [November 3, 2010]
• Panin_Walter_MSp.ps.gz (328885 bytes)

Ivan Panin <paniniv@gmail.com>
Charles Walter <Charles.Walter@unice.fr>