On the $L_{\infty}$-bialgebra structure of the rational homotopy groups $\pi_{*}(\Omega \Sigma Y)\otimes \mathbb{Q}$

Samson Saneblidze

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arXiv · 2311.15256

On the $L_{\infty}$-bialgebra structure of the rational homotopy groups $\pi_{*}(\Omega \Sigma Y)\otimes \mathbb{Q}$

Samson Saneblidze

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Abstract

We introduce the notion of an $L_{\infty}$-bialgebra structure on a vector space. We show that the rational homotopy groups $\pi_{*}(\Omega \Sigma Y)\otimes \mathbb{Q}$ admit such a structure for the loop space $\Omega \Sigma Y$ of a suspension $\Sigma Y$ that characterizes $Y$ up to rational homotopy equivalence.

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BibTeX RIS

Samson Saneblidze. 2023-11-26. On the $L_{\infty}$-bialgebra structure of the rational homotopy groups $\pi_{*}(\Omega \Sigma Y)\otimes \mathbb{Q}$. https://arxiv.org/abs/2311.15256

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