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

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 ratio...

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Published in:arXiv.org 2023-11
Main Author: Samson Saneblidze
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Language:English
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Vector spaces
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description 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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title On the \(L_{\infty}\)-bialgebra structure of the rational homotopy groups \(\pi_{}(\Omega \Sigma Y)\otimes \mathbb{Q}\)
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