On the homology of the space of singular knots

Hossein Abbaspour (1) , David Chataur (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LPP - Laboratoire Paul Painlevé - UMR 8524

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 nontriviality of the desingularization morphism.

Mots clés: knots; singular knots; long knots; free loops space; string operations

Domaines: Topologie algébrique [math.AT]; Topologie géométrique [math.GT]

Hossein Abbaspour, David Chataur. On the homology of the space of singular knots. Homology, Homotopy and Applications, 2013, 15 (1), pp.101-126. ⟨hal-00348675v2⟩