Mathematical Sciences: Algebraic and Geometric Topology

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T. Goodwillie will work on algebraic K-theory and its relation with equivariant stable homotopy theory. His previous work, using cyclic homology, was successful in reducing relative Waldhausen K-theory over the rationals to previously known theories. He will now attack a specific conjecture about relative Waldhausen K-theory (not over the rationals), and also address some more loosely formulated related questions. It is impressive how truly geometric are the underlying questions which give rise to the elaborate algebraic theories being considered.