Abstract
We study spaces of natural transformations between homogeneous functors in Goodwillie’s calculus of homotopy functors and in Weiss’s orthogonal calculus. We give a description of such spaces of natural transformations in terms of the homotopy fixed point construction. Our main application uses this description in combination with the Segal Conjecture to obtain a delooping theorem for connecting maps in the Goodwillie tower of the identity and in the Weiss tower of . The interest in such deloopings stems from conjectures made by the first and the third author [Filtered spectra arising from permutative categories, J. Reine Angew. Math. 604 (2007) 73-136] that these towers provide a source of contracting homotopies for certain projective chain complexes of spectra.
Citation
Gregory Z Arone. William G Dwyer. Kathryn Lesh. "Loop structures in Taylor towers." Algebr. Geom. Topol. 8 (1) 173 - 210, 2008. https://doi.org/10.2140/agt.2008.8.173
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