Skein modules of links in cylinders over surfaces
Jens Lieberum
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 $\mathbb Z[z]$-module $C(F \times [0,1])/\mathrm{Tor}(C(F \times [0,1]))$ 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 $F \times [0,1]$ where $F$ is an oriented surface with boundary.