Skein modules of links in cylinders over surfaces

Details Skein modules of links in cylinders over surfaces Skein modules of links in cylinders over surfaces

1999-11-23

arxiv.org/abs/math/9911174v2

Mathematics

Quantum Algebra

41 pages, 30 figures, new results added to previous version

Scientific paper

We define the Conway skein module C(M) of ordered based links in a 3-manifold M. This module gives rise to C(M)-valued invariants of usual links in M. We determine a basis of the Z[z]-module C(F x [0,1])/Tor(C(F x [0,1])) where F is the real projective plane or a surface with boundary. For cylinders over the Moebius strip or the projective plane we derive special properties of the Conway skein module, including a refinement of a theorem of Kawauchi and Hartley about the Conway polynomial of strongly positive amphicheiral knots in S^3. We also determine the Homfly and Kauffman skein modules of F x [0,1] where F is an oriented surface with boundary.

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