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Relations In The Homotopy Of Simplicial Abelian Hopf Algebras, James M. Turner

University Faculty Publications and Creative Works

In this paper, we analyze the structure possessed by the homotopy groups of a simplicial abelian Hopf algebra over the field F2. Specifically, we review the higher-order structure that the homotopy groups of a simplicial commutative algebra and simplicial cocommutative coalgebra possess. We then demonstrate how these structures interact under the added conditions present in a Hopf algebra.