ICM 1998, Berlin, Aug. 18--27 Abstracts of Plenary and Invited Lectures

s of Plenary and Invited Lectures Section: 6. Topology 1991 MS Classification: 57M Ohtsuki, Tomotada, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8552, Japan A filtration of the set of integral homology 3-spheres In 1989, Witten [3] proposed his famous formula of topological invariants of 3-manifolds, based on Chern-Simons gauge theory. The formula is given by using a path integral over all G connections on a 3-manifold, where G is a fixed Lie group. Following combinatorial properties of the invariants predicted by Witten's formula, the invariants, what we call the quantum G invariant, have been rigorously reconstructed by many researchers, say by using surgery presentations of 3-manifolds. Since we have many Lie groups, we have obtained many quantum invariants of 3-manifolds in this decade. To control these many invariants we consider the following two approaches. ffl Unify them into an invariant. ffl Chara..