2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106188Let $M$ be a closed oriented $d$-dimensionnal manifold and let $LM$ be the space of free loops on $M$. In this paper, we give a geometrical interpretation of the loop coproduct and we study it's compatibility with the Serre spectral sequence associated to the fibration $ΩM \to LM \to M$. Then, we show that the spectral sequence associated to the free loop fibration $LN \to LX \to LM$ of some Serre fibration $N \to X \to M$ is a spectral sequence of Frobenius algebra.11 pagesAlgebraic Topology55P35, 54N45, 55N33, 17A65, 81T30, 17B55text