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2011 Spectral sequences in string topology
Lennart Meier
Algebr. Geom. Topol. 11(5): 2829-2860 (2011). DOI: 10.2140/agt.2011.11.2829


In this paper, we investigate the behavior of the Serre spectral sequence with respect to the algebraic structures of string topology in generalized homology theories, specifically with the Chas–Sullivan product and the corresponding coproduct and module structures. We prove compatibility for two kinds of fiber bundles: the fiber bundle ΩnMLnMM for an h–oriented manifold M and the looped fiber bundle LnFLnELnB of a fiber bundle FEB of h–oriented manifolds. Our method lies in the construction of Gysin morphisms of spectral sequences. We apply these results to study the ordinary homology of the free loop spaces of sphere bundles and some generalized homologies of the free loop spaces of spheres and projective spaces. For the latter purpose, we construct explicit manifold generators for the homology of these spaces.


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Lennart Meier. "Spectral sequences in string topology." Algebr. Geom. Topol. 11 (5) 2829 - 2860, 2011.


Received: 8 June 2010; Revised: 12 September 2011; Accepted: 14 September 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1227.55007
MathSciNet: MR2846913
Digital Object Identifier: 10.2140/agt.2011.11.2829

Primary: 55P35 , 55T10
Secondary: 57R19

Keywords: free loop space , Gysin morphism , Serre spectral sequence , string topology

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.11 • No. 5 • 2011
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