Homology, Homotopy and Applications

Volume 15 (2013)

Number 1

On the homology of the space of singular knots

Pages: 101 – 126

DOI: https://dx.doi.org/10.4310/HHA.2013.v15.n1.a6


Hossein Abbaspour (Laboratoire Jean Leray, Université de Nantes, France)

David Chataur (Laboratoire Paul Painlevé, Université de Lille 1, Villeneuve d’Ascq, France)


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

Published 1 May 2013