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An \(E_{\infty}\) motivic \(2\)-cell complex and applications Gheorghe, Bogdan


By work of Hu-Kriz-Ormsby, Isaksen exhibits a motivic \(2\)-cell complex that has bigraded homotopy groups isomorphic to the classical Adams-Novikov \( E_2 \)-page for the sphere \( S^0 \). We show how to endow this \(2\)-cell complex with an \( E_{\infty}\)-ring structure, upgrading this isomorphism to an isomorphism of highly structured rings. We then show how to exploit this \(2\)-cell to construct a spectrum which we call \(wBP\), whose homotopy is polynomial in the new periodic motivic operators \(w_i\) introduced by Michael Andrews et al.

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