Operads and chain rules for the calculus of functors

Details Operads and chain rules for the calculus of functors Operads and chain rules for the calculus of functors

2009-02-03

arxiv.org/abs/0902.0399v2

Mathematics

Algebraic Topology

118 pages, NSF acknowledgement added

Scientific paper

We study the structure possessed by the Goodwillie derivatives of a pointed homotopy functor of based topological spaces. These derivatives naturally form a bimodule over the operad consisting of the derivatives of the identity functor. We then use these bimodule structures to give a chain rule for higher derivatives in the calculus of functors, extending that of Klein and Rognes. This chain rule expresses the derivatives of FG as a derived composition product of the derivatives of F and G over the derivatives of the identity. There are two main ingredients in our proofs. Firstly, we construct new models for the Goodwillie derivatives of functors of spectra. These models allow for natural composition maps that yield operad and module structures. Then, we use a cosimplicial cobar construction to transfer this structure to functors of topological spaces. A form of Koszul duality for operads of spectra plays a key role in this.

Affiliated with

Also associated with

No associations

Rating

Operads and chain rules for the calculus of functors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Operads and chain rules for the calculus of functors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Operads and chain rules for the calculus of functors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-296488