A skein module of links in cylinders over non-orientable surfaces
نویسنده
چکیده
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 . Let F = Σ× [0, 1] where Σ is the real projective plane or a surface with boundary. In this case C(F ) is in a natural way an algebra. We determine a basis of the Z[z]-module C#(F ) = C(F )/Tor(C(F )). When Σ is the Möbius strip or the projective plane we determine C#(F ) as an algebra and we prove that inside of C#(F ) and up to a sign a link is equal to its mirror image. The proofs contain a constructive algorithm for the computation of the link invariants corresponding to C#(F ). Mathematics Subject Classification (1991): 57M25
منابع مشابه
Skein Modules of Links in Cylinders over Surfaces
We define the Conway skein module (M) of ordered based links in a 3-manifold M . This module gives rise to (M)-valued invariants of usual links in M . We determine a basis of the Z[z]-module (Σ× [0,1])/Tor( (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 mo...
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