An algebraic model for the loop space homology of a homotopy fiber

Details An algebraic model for the loop space homology of a homotopy fiber An algebraic model for the loop space homology of a homotopy fiber

2004-10-23

arxiv.org/abs/math/0410503v4

Mathematics

Algebraic Topology

Introduction revised, some reorganization, 54 pages

Scientific paper

Let F denote the homotopy fiber of a map f:K-->L of 2-reduced simplicial sets. Using as input data the strongly homotopy coalgebra structure of the chain complexes of K and L, we construct a small, explicit chain algebra, the homology of which is isomorphic as a graded algebra to the homology of GF, the simplicial (Kan) loop group on F. To construct this model, we develop machinery for modeling the homotopy fiber of a morphism of chain Hopf algebras. Essential to our construction is a generalization of the operadic description of the category DCSH of chain coalgebras and of strongly homotopy coalgebra maps given in (math.AT/0505559) to strongly homotopy morphisms of comodules over Hopf algebras. This operadic description is expressed in terms of a general theory of monoidal structures in categories with morphism sets parametrized by co-rings, which we elaborate here.

Affiliated with

Also associated with

No associations

Rating

An algebraic model for the loop space homology of a homotopy fiber 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 An algebraic model for the loop space homology of a homotopy fiber, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An algebraic model for the loop space homology of a homotopy fiber will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-485355