Loop Structures In Taylor Towers
| Venue: | ALGEBRAIC & GEOMETRIC TOPOLOGY |
BibTeX
@MISC{Arone_loopstructures,
author = {G. Z. Arone and W. G. Dwyer and K. Lesh},
title = {Loop Structures In Taylor Towers},
year = {}
}
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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 is a delooping theorem for connecting maps in the Goodwillie tower of the identity and in the Weiss tower of BU(V). The interest in such deloopings stems from conjectures made by the first and the third author [4] that these towers provide a source of contracting homotopies for certain projective chain complexes of spectra.
Citations
| 122 | Model categories. Mathematical Surveys and Monographs, 63 - Hovey - 1999 |
| 94 | Model categories of diagram spectra - Mandell, May, et al. |
| 25 | The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres - Arone, Mahowald - 1999 |
| 16 | Calculus III: Taylor Series - Goodwillie - 2003 |
| 16 | Equivalences of monoidal model categories - Schwede, Shipley |
| 15 | Function complexes of diagrams of simplicial sets - Dwyer, Kan |
| 13 | Partition complexes, Tits buildings and symmetric products - Arone, Dwyer |
| 12 | Product and other fine structure in polynomial resolutions of mapping spaces - Ahearn, Kuhn |
| 8 | A Kahn-Priddy sequence and a conjecture of - Kuhn - 1982 |
| 7 | The transfer and Whitehead’s conjecture - Kuhn, Priddy - 1985 |
| 2 | The Weiss derivatives of - Arone |
| 2 | Filtered spectra arising from permutative categories - Arone, Lesh |
| 1 | K –localizations and K –equivalences of infinite loop spaces - Bousfield - 1982 |
