String spectral sequence

Abstract

We define shriek map for a finite codimensionnal embedding of fibration. We study the morphisms induced by shriek maps in the Leray-Serre spectral sequence. As a byproduct, we get two multiplicative spectral sequences of algebra wich converge to the Chas and Sullivan algebra ${\mathbb{H}}_{\ast }(LE)$ of the total space $E$ of a fibration. We apply this technic to find some result on the intersection morphism $I:{\mathbb{H}}_{\ast }(LE)⟶H_{\ast }(\Omega E)$ and to the space of free paths on a manifold $M^I$.

16 pages Add some new results at the preceding version titled "Chas and Sullivan algebra of fiber bundles"