Abstract
We use the Jaco-Shalen and Johannson theory of the characteristic submanifold and the Torus theorem (Gabai, Casson-Jungreis) to develop an intrinsic finite type theory for knots in irreducible 3-manifolds. We also establish a relation between finite type knot invariants in 3-manifolds and these in R 3. As an application we obtain the existence of non-trivial finite type invariants for knots in irreducible 3-manifolds.
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