Algebraic groups of homotopy classes of automorphisms and operadic Koszul duality

Bashar Saleh

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arXiv · 2305.02076

Algebraic groups of homotopy classes of automorphisms and operadic Koszul duality

Bashar Saleh

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Abstract

Given a simply connected space $X$, there are several, a priori different, algebraic groups whose groups of $\mathbb Q$-points are isomorphic to the group of homotopy classes of homotopy automorphisms of the rationalization of $X$. We will show that two of these different algebraic groups are isomorphic using the theory of operadic Koszul duality. As a by-product of the techniques we use, we deduce some isomorphisms of sets of homotopy classes of maps that might be viewed as Eckmann-Hilton dual to some well-known isomorphisms.

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Bashar Saleh. 2023-05-03. Algebraic groups of homotopy classes of automorphisms and operadic Koszul duality. https://arxiv.org/abs/2305.02076

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