#### Volume 9, issue 2 (2009)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Homology of spaces of regular loops in the sphere

### David Chataur and Jean-François Le Borgne

Algebraic & Geometric Topology 9 (2009) 935–977
##### 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