UNIVERSAL VASSILIEV INVARIANTS OF LINKS IN COVERINGS OF 3-MANIFOLDS

Abstract

We study Vassiliev invariants of links in a 3-manifold M by using chord diagrams labeled by elements of the fundamental group of M. We construct universal Vassiliev invariants of links in M, where M=P ²×[0,1] is a cylinder over the real projective plane P ², M=Σ×[0,1] is a cylinder over a surface Σ with boundary, and M=S ¹×S ². A finite covering p:N→M induces a map π ₁(p)* between labeled chord diagrams that corresponds to taking the preimage p ^-1(L)⊂N of a link L⊂M. The maps p ^-1 and π ₁(p)* intertwine the constructed universal Vassiliev invariants.