Title: A Filtration of the Set of Integral Homology 3-Spheres

A filtration on the set of integral homology 3-spheres is introduced, based on the universal perturbative invariant (the LMO invariant) or equivalently based on finite type invariants of integral homology 3-spheres. We also survey on these invariants related to quantum invariants.

1991 Mathematics Subject Classification: 57M

Keywords and Phrases: integral homology 3-spheres, knots, finite type invariant, quantum invariant, Kontsevich invariant, Vassiliev invariant

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