The Lawrence-Sullivan construction is the right model of $I^+$

TL;DR

This paper demonstrates that the Lawrence-Sullivan construction accurately models the algebraic structure of $I^+$ by relating it to the Baues-Lemaire cylinder and derives a generalized Euler formula for Bernoulli numbers.

Contribution

It establishes the Lawrence-Sullivan construction as the correct model of $I^+$ and connects it to the Baues-Lemaire cylinder, providing new insights into algebraic topology.

Findings

The universal enveloping algebra of the Lawrence-Sullivan construction is a perturbation of the Baues-Lemaire cylinder.

The Lawrence-Sullivan construction is validated as the right model of $I^+$.

A generalized Euler formula on Bernoulli numbers is deduced.

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 evidences we present, this exhibits the Lawrence-Sullivan construction as the right model of $I^+$. From this, we also deduce a generalized Euler formula on Bernoulli numbers.