Various Aspects of Topology

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Topology is the mathematics to study the position and the shape. The development of topology in the last decade was promoted by the interaction between the branches of topology as well as that between differential geometry, algebra, analysis, mathematical physics and topology. In this research, we wish to promote the development much more. We did the researches in the following fields : classifying theory of singularities of mappings and algebraic varieties, various group actions on manifolds and simplicial complexes, the action of the mapping class groups of the surfaces on their Teichmuller spaces, the dynamical study of complex analytic maps, the dynamical study of vector fields on manifolds and foliations, the classifying theory of hyperbolic 3 dimensional manifolds and hyperbolic spaces with singularities, the differentiable structures and symplectic structures on 4 dimensional manifolds, the conformal field theory and invariants of dimensional manifolds, the topology of the moduli spaces of connections of various principal bundles, the Poisson manifolds and contact manifolds, equivariant generalized (co)homology theories and homotopy theories, invariants of knots and links and their classification, general topology theory for wild spaces. These researches were done successfully with their own results. In order to promote the interaction between these researches we held "Topology Symposium" each year as well as many conferences on the above research fields. These are done as Topology Projects in the collaboration with researchers in topology in Japan. In particular, the series of the meetings "Encounter with Mathematics" were held in order to promote the interaction with researchers in other fields as well as graduate students. By these research activities, the direction of new development for the next project became clear.