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

Abstract

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.

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

References in corpus (6)

• Operads and Motives in Deformation Quantization
• Integral Invariants of 3-Manifolds. II
• Integral Expressions for the Vassiliev Knot Invariants
• On a Universal Invariant of 3-Manifolds
• Rationality Results for the Configuration Space Integral of Knots
• Finite type invariants, the mapping class group and blinks

Cited by in corpus (25)

• Remarks on Chern-Simons invariants
• Chern-Simons theory, analytic continuation and arithmetic
• Splitting formulae for the Kontsevich-Kuperberg-Thurston invariant of rational homology 3-spheres
• Analyticity of the Free Energy of a Closed 3-Manifold
• On the Kontsevich-Kuperberg-Thurston construction of a configuration-space invariant for rational homology 3-spheres
• Surgery formulae for finite type invariants of rational homology 3--spheres
• On the cube of the equivariant linking pairing for knots and 3-manifolds of rank one
• Feynman integrals and motives of configuration spaces
• Some exotic nontrivial elements of the rational homotopy groups of $\mathrm{Diff}(S^4)$
• Theta-graph and diffeomorphisms of some 4-manifolds
• Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing
• On homotopy invariants of combings of 3-manifolds
• Beads: From Lie algebras to Lie groups
• New perspectives on self-linking
• A note on Jones polynomial and cosmetic surgery
• Knot invariants derived from the equivariant linking pairing
• Morse theory and Lescop's equivariant propagator for 3-manifolds with $b_1=1$ fibered over $S^1$
• Manifold theoretic compactifications of configuration spaces
• A combinatorial definition of the Theta-invariant from Heegaard diagrams
• Garoufalidis-Levine's finite type invariants for $\mathbb{Z}\pi$-homology equivalences from 3-manifolds to the 3-torus
• Higher order generalization of Fukaya's Morse homotopy invariant of 3-manifolds I. Invariants of homology 3-spheres
• On the vanishing of the Rokhlin invariant
• A survey of Bott-Taubes integration
• Addendum to: Some exotic nontrivial elements of the rational homotopy groups of $\mathrm{Diff}(S^4)$ (homological interpretation)
• On Kontsevich's characteristic classes for smooth 5- and 7-dimensional homology sphere bundles