1. Infinite symmetric products of rational algebras and spaces
- Author
-
Hu, Jiahao and Milivojević, Aleksandar
- Subjects
Symmetric products ,Dold–Thom theorem ,Mathematics ,QA1-939 - Abstract
We show that the infinite symmetric product of a connected graded-commutative algebra over $\mathbb{Q}$ 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 $\mathbb{Q}$ 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 show that finite symmetric products of certain simple free graded-commutative algebras are free; this allows us to determine minimal Sullivan models for finite symmetric products of complex projective spaces.
- Published
- 2022
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