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Thursday, March 19, 2015

**Abstract:** I will show that the derivatives of a functor from based spaces to spectra have a K(E_n)-action (from which the Taylor tower can be reconstructed) if and only if the functor is represented on a certain category of `pointed framed n-dimensional manifolds'. The main example of interest will be Waldhausen's A(X) which we show to be represented on pointed framed 3-manifolds. Ultimately, this depends on the fact that the pth power map from S^1 to S^1 can be realized as a framed map between solid tori. This is joint work with Greg Arone.