Finite type invariants of 3-manifolds

Details Finite type invariants of 3-manifolds Finite type invariants of 3-manifolds

1998-05-06

arxiv.org/abs/math/9805026v2

Inventiones Math. 140 (2000), 45-100

Mathematics

Geometric Topology

Final version for publication, with figures. The most significant changes from the original posted version are in the expositi

Scientific paper

A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for manifolds with large first betti number, encompassing much of the complexity of Ohtsuki's theory for homology spheres. (For example, it is seen that the quantum SO(3) invariants, though not of finite type, are determined by finite type invariants.) The algebraic structure of the set of all finite type invariants is investigated, along with a combinatorial model for the theory in terms of trivalent "Feynman diagrams".

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