Normalisation for the fundamental crossed complex of a simplicial set

Details Normalisation for the fundamental crossed complex of a simplicial set Normalisation for the fundamental crossed complex of a simplicial set

2006-11-23

arxiv.org/abs/math/0611728v2

Mathematics

Algebraic Topology

29 pages, accepted for JHRS Mac Lane memorial volume Revised Jan 2007. Minor points. More references

Scientific paper

Crossed complexes are shown to have an algebra sufficiently rich to model the geometric inductive definition of simplices, and so to give a purely algebraic proof of the Homotopy Addition Lemma (HAL) for the boundary of a simplex. This leads to the {\it fundamental crossed complex} of a simplicial set. The main result is a normalisation theorem for this fundamental crossed complex, analogous to the usual theorem for simplicial abelian groups, but more complicated to set up and prove, because of the complications of the HAL and of the notion of homotopies for crossed complexes. We start with some historical background, {and give a survey of the required basic facts on crossed complexes.}

Affiliated with

Also associated with

No associations

Rating

Normalisation for the fundamental crossed complex of a simplicial set 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 Normalisation for the fundamental crossed complex of a simplicial set, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Normalisation for the fundamental crossed complex of a simplicial set will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-700698