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On the relation of symplectic algebraic cobordism to hermitian K-theory

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00531734
Contributor : Charles Walter <>
Submitted on : Wednesday, November 3, 2010 - 4:13:04 PM
Last modification on : Monday, October 12, 2020 - 10:27:28 AM

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  • HAL Id : hal-00531734, version 1
  • ARXIV : 1011.0652

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Ivan Panin, Charles Walter. On the relation of symplectic algebraic cobordism to hermitian K-theory. 2010. ⟨hal-00531734⟩

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