Cross-effects and the classification of Taylor towers
Number of Authors: 2
2016 (English)In: Geometry and Topology, ISSN 1465-3060, E-ISSN 1364-0380, Vol. 20, no 3, 1445-1537 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2016. Vol. 20, no 3, 1445-1537 p.
IdentifiersURN: urn:nbn:se:su:diva-135081DOI: 10.2140/gt.2016.20.1445ISI: 000384753100006OAI: oai:DiVA.org:su-135081DiVA: diva2:1048991