Deformation of string topology into homotopy skein modules

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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M35, 57R42

References

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Publication

Received: 20 2003

Accepted: 8 October 2003

Published: 11 October 2003

Authors

Uwe Kaiser
Department of Mathematics Boise State University 1910 University Drive Boise, ID 83725-1555 USA
http://diamond.boisestate.edu/~kaiser/

Volume 3, issue 2 (2003)

Uwe Kaiser