Deformation of string topology into homotopy skein modules

Kaiser, Uwe¹

¹Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725-1555, USA

Algebraic and Geometric Topology, Tome 3 (2003) no. 2, pp. 1005-1035

Résumé

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.

Détail

DOI : 10.2140/agt.2003.3.1005

Keywords: $3$–manifold, string topology, deformation, skein module, torsion, link homotopy, free loop space, Lie algebra

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