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Skein modules of links in cylinders over surfaces

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  • Jens Lieberum

Abstract

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 ( Σ × [ 0 , 1 ] ) / Tor ( 𝒞 ( Σ × [ 0 , 1 ] ) ) , where Σ is the real projective plane or a surface with boundary. For cylinders over the Möbius strip or the projective plane, we derive special properties of the Conway skein module, among them a refinement of a theorem of Hartley and Kawauchi about the Conway polynomial of strongly positive amphicheiral knots in S 3 . In addition, we determine the Homfly and Kauffman skein modules of Σ × [ 0 , 1 ] where Σ is an oriented surface with boundary.

Suggested Citation

  • Jens Lieberum, 2002. "Skein modules of links in cylinders over surfaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 32, pages 1-40, January.
    • Handle: RePEc:hin:jijmms:579210
    DOI: 10.1155/S016117120201181X
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