SKEIN MODULES OF LINKS IN CYLINDERS OVER SURFACES

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(F × [0, 1])/Tor(C(F × [0, 1])) where F 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, 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 × [0, 1] where F is an oriented surface with boundary.