Deformation of string topology and skein modules of oriented 3-manifolds

Uwe Kaiser

KNOTS in WASHINGTON XV (2nd Japan-USA Workshop in Knot Theory)
January 10-15, 2003
George Washington University and Johns Hopkins University
Washington, DC and Baltimore, MD, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Shin-ichi Suzuki, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

Conference Homepage

Deformation of string topology and skein modules of oriented 3-manifolds
by
Uwe Kaiser
Boise State University

Recently Moira Chas and Dennis Sullivan discovered interesting algebraic structures on the S¹-equivariant homology of the space of maps from S¹ into a d-dimensional smooth oriented manifold M. There is a natural approach of a geometric deformation of these structures for d=3. It replaces free homotopy classes of loops by isotopy classes of links and deforms coefficients at the same time. The relation of deformations with the theory of link homotopy skein modules is discussed. For the q-homotopy skein module naturally defined twisted string topology pairings are necessary. For isotopy skein modules the self-intersection component can be related to coalgebra structures on string homology and its generalizations.

Date received: November 26, 2002