Homology, Homotopy and Applications
Volume 15 (2013)
On the homology of the space of singular knots
Pages: 101 – 126
In this paper we introduce various associative products on the homology of the space of knots and singular knots in $S^n$. We prove that these products are related through a desingularization map. We also compute some of these products and prove the non-triviality of the desingularization morphism. Using direct computations, we prove that some of these products are indeed commutative.
knot, singular knot, long knot, free loop space, string operation, chord diagram
2010 Mathematics Subject Classification
55N45, 55P50, 57Q45