Mathematical Sciences: Research in Topology

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8901213 Cappell This project includes research problems in a variety of areas of geometrical topology. These include singular spaces and their characteristic classes, transformation groups and H-spaces, some questions in low-dimensional topology and nonlinear similarity. Among the specific problems are questions related to the role of K-homology characteristic classes on singular spaces and methods of computing them; characteristic classes on singular algebraic varieties and methods of computing them; Alexander polynomials of nonisolated singularities; replacement of fixed points of group actions; de Rham's problem on similarity of matrices. These topics concern the possible reduction to a certain amount of computation of questions about knottedness, connectedness, and so forth. The ultimate subject matter of topology is the latter, but systematic treatment requires the introduction of algebraic concepts such as groups and rings and of techniques for computing with them.