A filtration of the set of integral homological 3-spheres
The author reviews the Kontsevich and Vassiliev invariants for \(3\)-manifolds and discusses a universal perturbative invariant, the LMO invariant. This invariant can be expressed as the exponential of a linear sum of connected web diagrams and is universal among perturbative and finite type invariants. Two integral homology spheres are defined to be \(d\)-equivalent if all their finite type invariants of degree \(<d\) agree. This induces a filtration on the sets of equivalence classes of \(\mathbb Z\)-homology spheres.
scientific article; zbMATH DE number 1184325
scientific article