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arXiv · 1404.1417

Cross-effects and the classification of Taylor towers

Gregory Arone·Michael Ching
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Abstract

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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BibTeXRIS

Gregory Arone, Michael Ching. 2014-04-05. Cross-effects and the classification of Taylor towers. https://doi.org/10.2140/gt.2016.20.1445

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