Synthetic Studies ofTopology

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Recent progress of topology is prompted by the recognition of its relationship with the other area of mathematics which includes differential Geometry, algebra, analysis and mathematical physics. This makes the method of investigation more sophisticated and gives the researches wider perspectives. The purpose of this research project is to make cooperation of various researchers easy and timingly, making the field more active .We have successfully maintained the network of topologists, organized various symposia and conferences timingly, did exchanges of the researchers, invited various well recognized foreign researchers, gave many colloquia abroad, thus contributing to the development of topology in a significant way.Concretely the research of the following areas of topology is developed by our research projects: Theory of singularities of algebraic and differentiable maps: Group actions on manifolds and on simplicial complexes: Actions of mapping class groups on Teichmuller spaces of the surface: Theory of dynamical systems of complex analytic maps: Dynamical study of vector fields on manifolds and foliation theory: Geometirc study of hyperbolic 3-manifold: Differential structure of 4-manifolds and symplectic structures: Conformal field theory: Homotopy theory: Invariants of knots and links: General topology especially those concerned with wild spaces.In Japan, topology is developing constantly by the efforts of many researchers, and it gained worldwide recognition.Grant in aid by the Japan Society for the Promotion of Science is indispensable in this development. We express our hearty gratitude to the JSPS.