Non-Formality of $S^2$ via the free loop space

Ryan McGowan, Florian Naef, Brian O'Callaghan

We show that the $E_1$-equivalence $C^{\bullet }(S^2)\simeq H^{\bullet }(S^2)$ does not intertwine the inclusion of constant loops into the free loop space $S^2\to L{S}^2$. That is, the…