Mathematical Sciences: Algebraic Problems Connected with Homology of Groups, Fixed Point Theory and Shape

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Professor Geoghegan will investigate two kinds of problems on the borderline between topology and algebra. The first set of problems concerns developments of his recent work with A. Nicas on one-parameter fixed point theory. They recently found a "higher trace" in Hochschild homology which faithfully detects the primary obstruction to removing circles of fixed points from a homotopy. They will now investigate the algebra surrounding the remaining geometric obstructions, as well as related matters. The second set of problems concerns higher order end theory of groups. He will investigate various topological end invariants of a group which should detect interesting properties of the group itself.