Homology of spaces of regular loops in the sphere

Details Homology of spaces of regular loops in the sphere Homology of spaces of regular loops in the sphere

2008-11-20

arxiv.org/abs/0811.3319v2

Mathematics

Algebraic Topology

32 pages, 12 figures

Scientific paper

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

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