Homology of spaces of regular loops in the sphere

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.