Moduli of suspension spectra
Abstract
Description
For a 1-connected spectrum E, we study the moduli space of suspension spectra which come equipped with a weak equivalence to E. We construct a spectral sequence converging to the homotopy of the moduli space in positive degrees. In the metastable range, we get a complete homotopical classification of the path components of the moduli space. Our main tool is Goodwillie's calculus of homotopy functors.
24 pages. In this version (hopefully the last), I've added an appendix which explains the classification of quadratic homotopy functors from spectra to spectra (I learned about these ideas from Goodwillie and Kuhn). The classification can be used to give a more concrete description of the main invariant in the paper
24 pages. In this version (hopefully the last), I've added an appendix which explains the classification of quadratic homotopy functors from spectra to spectra (I learned about these ideas from Goodwillie and Kuhn). The classification can be used to give a more concrete description of the main invariant in the paper