Deformation of string topology into homotopy skein modules

Abstract

Relations between the string topology of Chas and Sullivan and the homotopy skein modules of Hoste and Przytycki are studied. This provides new insight into the structure of homotopy skein modules and their meaning in the framework of quantum topology. Our results can be considered as weak extensions to all orientable 3-manifolds of classical results by Turaev and Goldman concerning intersection and skein theory on oriented surfaces.