Homology of spaces of regular loops in the sphere

Chataur, David; Le Borgne, Jean-François

doi:10.2140/agt.2009.9.935

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Homology of spaces of regular loops in the sphere

David Chataur and Jean-François Le Borgne

Algebraic & Geometric Topology 9 (2009) 935–977

DOI: 10.2140/agt.2009.9.935

Abstract

In this paper we compute the singular homology of the space of immersions of the circle into the $n$ –sphere. Equipped with the Chas–Sullivan loop product these homology groups are graded commutative algebras, which we also compute. We enrich Morse spectral sequences for fibrations of free loop spaces together with loop products. This offers some new computational tools for string topology.

Keywords

free loop space, immersion space, string operation, Morse theory, spectral sequence

Mathematical Subject Classification 2000

Primary: 55N45, 58E05

References

Publication

Received: 25 November 2008

Revised: 26 March 2009

Accepted: 30 March 2009

Published: 8 May 2009

Authors

David Chataur
Laboratoire Paul Painlevé Département de Mathématiques Université de Lille1 59655 Villeneuve d’Ascq France

Jean-François Le Borgne
Laboratoire Paul Painlevé Département de Mathématiques Université de Lille1 59655 Villeneuve d’Ascq France

Volume 9, issue 2 (2009)