String spectral sequence

2004/09/30 by Le Borgne, Borgne, Le
Mathematics · #17A65 #17B55 #54N45 #55N33 #55P35 #81T30 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:17A65 #msc:17B55 #msc:54N45 #msc:55N33 #msc:55P35 #msc:81T30

paper · pdf · doi:10.48550/arxiv.math/0409597

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

arxiv created 2005/01/06 · arxiv updated 2009/12/01

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 ℍ_*(LE) of the total space E of a fibration. We apply this technic to find some result on the intersection morphism I: ℍ_*(LE) \longrightarrow H_*(ΩE) and to the space of free paths on a manifold M^I.

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