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Loop structures in Taylor
towers
Gregory Z Arone, William G Dwyer and Kathryn Lesh |
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Algebraic & Geometric Topology 8 (2008) 173–210
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Abstract |
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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. |
Keywords
derived natural transformations, Whitehead Conjecture,
homotopy calculus, orthogonal calculus, homogeneous
functors, delooping, Segal Conjecture
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Mathematical Subject Classification 2000
Primary: 55P65
Secondary: 55P47, 18G55
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References |
Publication
Received: 24 April 2007
Revised: 30 November 2007
Accepted: 19 December 2007
Published: 8 February 2008
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Authors |
| Gregory Z Arone | |
| Kerchof Hall University of Virginia PO Box 400137 Charlottesville VA 22904 USA |
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| http://www.math.virginia.edu/~zga2m/ | |
| William G Dwyer | |
| Department of Mathematics University of Notre Dame Notre Dame IN 46556 USA |
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| http://www.nd.edu/~wgd/ | |
| Kathryn Lesh | |
| Department of Mathematics Union College Schenectady NY 12309 USA |
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| http://www.math.union.edu/~leshk/ | |
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