Deformation of cone-manifolds and topology of 3-mainfolds

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The aim of this project was to develop the deformation theory of cone-manifolds from interdisciplinary viewpoints and to apply it to the theory of topology of 3-manifolds, base on our previous related works.The starting point was the workshop "Cone-manifolds and hyperbolic geometry" which we held on July '98 at Tokyo Institute of Technology. Summarizing related works up to those days, we reconfirmed an attraction and power of the deformation method of cone structures. Then reflecting on much attention for geometric understanding of Dehn fillings in the workshop, we have developed the theory of deformation of cone structures and topology of 3-manifolds, emphasizing the connection with gauge theory, mapping classes, collapsings, Kleinian groups and quantum invariants, by having many discussions and small intensive meetings for two years. We also printed a few informal booklets which collected several research drafts, and distributed them to the institutions and researchers for their convenience. The concluding symposium "geometric topology of 3-manifolds" on January '00 summarized the results on 3-manifolds by geometric method in the last two years and discussed the prospect of the research.There are many interactions between several aspects of 3-manifolds recently and the study of 3-manifolds by geometric method seems to get into new stage. In view of these circumstance, our project clarified that geometric method in finding mathematical structures behind appearance became important for the future in which presentations of characteristics would interact more.