String spectral sequence

Details String spectral sequence String spectral sequence

2004-09-30

arxiv.org/abs/math/0409597v2

Mathematics

Algebraic Topology

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

Scientific paper

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 $I: \mathbb{H}_*(LE) \longrightarrow H_*(\Omega E)$ and to the space of free paths on a manifold $M^I$.

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