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

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.