Geodesic
On the relation of special linear algebraic cobordism to Witt groups
Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 205-230.

Voir la notice de l'article provenant de la source International Press of Boston

We reconstruct derived Witt groups via special linear algebraic cobordism. There is a morphism of ring cohomology theories that sends the canonical Thom class in special linear cobordism to the Thom class in the derived Witt groups. We show that for every smooth variety $X$, this morphism induces an isomorphism\[{\mathrm{MSL}}_{\eta *}^{[\star]}(X)\otimes_{{\mathrm{MSL}}^{[2\star]}_{\hphantom{[}0}({\rm pt})}\mathrm{W}^{2\star}({\rm pt}) \to \mathrm{W}^\star(X)[\eta,\eta^{-1}],\]where $\eta$ is the stable Hopf map. This result is an analogue of the result by Panin and Walter reconstructing hermitian $K$-theory using symplectic algebraic cobordism.
DOI : 10.4310/HHA.2016.v18.n1.a11
Classification : 14F42, 19E20, 19G12, 19G38
Keywords: Witt groups, algebraic cobordism, SL-oriented cohomology, Hopf map 
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     title = {On the relation of special linear algebraic cobordism to {Witt} groups},
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     pages = {205--230},
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Alexey Ananyevskiy. On the relation of special linear algebraic cobordism to Witt groups. Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 205-230. doi : 10.4310/HHA.2016.v18.n1.a11. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a11/

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