Mathematics – Algebraic Topology
Scientific paper
2005-01-25
Geom. Topol. 9(2005) 833-933
Mathematics
Algebraic Topology
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper20.abs.html Version 3: Reference to Salv
Scientific paper
We describe a cooperad structure on the simplicial bar construction on a reduced operad of based spaces or spectra and, dually, an operad structure on the cobar construction on a cooperad. We also show that if the homology of the original operad (respectively, cooperad) is Koszul, then the homology of the bar (respectively, cobar) construction is the Koszul dual. We use our results to construct an operad structure on the partition poset models for the Goodwillie derivatives of the identity functor on based spaces and show that this induces the `Lie' operad structure on the homology groups of these derivatives. We also extend the bar construction to modules over operads (and, dually, to comodules over cooperads) and show that a based space naturally gives rise to a left module over the operad formed by the derivatives of the identity.
No associations
LandOfFree
Bar constructions for topological operads and the Goodwillie derivatives of the identity 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 Bar constructions for topological operads and the Goodwillie derivatives of the identity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bar constructions for topological operads and the Goodwillie derivatives of the identity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-513608