Mathematical Sciences: Some Problems in 3-Dimensional Topology and in Related Algebra

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9626537 Scott Scott plans to continue work on his book on the theory of 3-manifolds. He also intends to explore further some recent work done jointly with G. A. Swarup of the University of Melbourne, Australia. They have found an algebraic version of the Annulus Theorem from the theory of 3-manifolds, and there are several different directions of inquiry that they plan to pursue. Their ideas involve new applications of some earlier work of Scott and are closely related to important work in the theory of 3-manifolds and in geometric group theory. These ideas should simplify some difficult recent work of other authors and prove new results that have been impossible to prove with the available techniques. The theme of this project is the close connection between certain types of geometry and group theory. It brings together ideas of several authors in these different areas that at first seemed to apply only in special situations but are now being seen to be connected and to have much more general applicability. ***