English

String spectral sequence

Algebraic Topology 2007-05-23 v2

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)\mathbb{H}_*(LE) of the total space EE of a fibration. We apply this technic to find some result on the intersection morphism I:H(LE)H(ΩE)I: \mathbb{H}_*(LE) \longrightarrow H_*(\Omega E) and to the space of free paths on a manifold MIM^I.

Keywords

Cite

@article{arxiv.math/0409597,
  title  = {String spectral sequence},
  author = {Le Borgne},
  journal= {arXiv preprint arXiv:math/0409597},
  year   = {2007}
}

Comments

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