String spectral sequence
Abstract
Description
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 $\mathbb{H}_*(LE)$ of the total space $E$ of a fibration. We apply this technic to find some result on the intersection morphism $I: \mathbb{H}_*(LE) \longrightarrow H_*(ΩE)$ 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"
16 pages Add some new results at the preceding version titled "Chas and Sullivan algebra of fiber bundles"