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2016 Cross-effects and the classification of Taylor towers
Gregory Arone, Michael Ching
Geom. Topol. 20(3): 1445-1537 (2016). DOI: 10.2140/gt.2016.20.1445


Let F be a homotopy functor with values in the category of spectra. We show that partially stabilized cross-effects of F have an action of a certain operad. For functors from based spaces to spectra, it is the Koszul dual of the little discs operad. For functors from spectra to spectra it is a desuspension of the commutative operad. It follows that the Goodwillie derivatives of F are a right module over a certain “pro-operad”. For functors from spaces to spectra, the pro-operad is a resolution of the topological Lie operad. For functors from spectra to spectra, it is a resolution of the trivial operad. We show that the Taylor tower of the functor F can be reconstructed from this structure on the derivatives.


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Gregory Arone. Michael Ching. "Cross-effects and the classification of Taylor towers." Geom. Topol. 20 (3) 1445 - 1537, 2016.


Received: 14 April 2014; Revised: 30 March 2015; Accepted: 18 July 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1350.55018
MathSciNet: MR3523062
Digital Object Identifier: 10.2140/gt.2016.20.1445

Primary: 55P48, 55P65
Secondary: 18D50

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.20 • No. 3 • 2016
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