Homology, Homotopy and Applications

Volume 15 (2013)

Number 1

On the homology of the space of singular knots

Pages: 101 – 126

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

Authors

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

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

Abstract

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.

Keywords

knot, singular knot, long knot, free loop space, string operation, chord diagram

2010 Mathematics Subject Classification

55N45, 55P50, 57Q45

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