# Infinite symmetric products of rational algebras and spaces

@article{Hu2022InfiniteSP, title={Infinite symmetric products of rational algebras and spaces}, author={Jiahao Hu and Aleksandar Milivojevi'c}, journal={Comptes Rendus. Math{\'e}matique}, year={2022} }

We show that the infinite symmetric product of a connected graded-commutative algebra overQ is naturally isomorphic to the free graded-commutative algebra on the positive degree subspace of the original algebra. In particular, the infinite symmetric product of a connected commutative (in the usual sense) graded algebra over Q is a polynomial algebra. Applied to topology, we obtain a quick proof of the Dold–Thom theorem in rational homotopy theory for connected spaces of finite type. We also…

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