TYPE-1 KNOT INVARIANTS IN 3-MANIFOLDS

The general theory of knotting in 3-manifolds has recently seen signif icant progress. One important aspect of this has been the effort towar d generalizing the notion of finite type invariants from S-3 to arbitr ary 3-manifolds. Here we will present a new class of finite type invar iants, defined in arbitrary orientable 3-manifolds, that are both simp le to define and to compute. They will be seen to be of both practical utility, in distinguishing large families of knots, and also of theor etical interest, giving access to subtle unknotting results.