The Lawrence–Sullivan construction is the right model for $I^+$

Abstract

We prove that the universal enveloping algebra of the Lawrence–Sullivan construction is a particular perturbation of the complete Baues–Lemaire cylinder of $S^0$. Together with other evidence we present, this exhibits the Lawrence–Sullivan construction as the right model for $I^{+}$. From this, we also deduce a generalized Euler formula on Bernoulli numbers.