#### Volume 8, issue 1 (2008)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Loop structures in Taylor towers

### Gregory Z Arone, William G Dwyer and Kathryn Lesh

Algebraic & Geometric Topology 8 (2008) 173–210
##### 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 $BU\left(V\right)$. 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
##### Mathematical Subject Classification 2000
Primary: 55P65
Secondary: 55P47, 18G55