Homology of spaces of regular loops in the sphere

2008/11/20 by Chataur, David, Borgne, Jean-Francois Le
#53C22 #55N45 #55T05 #55T10 #57R19 #57R42 #57R70 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0811.3319

Abstract

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.

Related

• The loop homology algebra of spheres and projective spaces
• A homotopy theoretic realization of string topology
• Configuration spaces on the sphere and higher loop spaces
• Symplectic A_∞-algebras and string topology operations
• Cell attachments and the homology of loop spaces and differential graded algebras