Perturbative 3-manifold invariants by cut-and-paste topology

Details Perturbative 3-manifold invariants by cut-and-paste topology Perturbative 3-manifold invariants by cut-and-paste topology

1999-12-21

arxiv.org/abs/math/9912167v2

Mathematics

Geometric Topology

18 pages, many figures. The important change in this version is an improved blowup construction. Also 20-30 typos have been co

Scientific paper

We give a purely topological definition of the perturbative quantum invariants of links and 3-manifolds associated with Chern-Simons field theory. Our definition is as close as possible to one given by Kontsevich. We will also establish some basic properties of these invariants, in particular that they are universally finite type with respect to algebraically split surgery and with respect to Torelli surgery. Torelli surgery is a mutual generalization of blink surgery of Garoufalidis and Levine and clasper surgery of Habiro.

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