Abstract
We introduce the notion of a closed necklical set in order to describe a functorial combinatorial model of the free loop fibration ΩY→ΛY→Y over the geometric realization Y=|X| of a path‐connected simplicial set X. In particular, to any path‐connected simplicial set X we associate a closed necklical set Λ̂X such that its geometric realization |Λ̂X|, a space built out of glueing ‘freehedrical’ and ‘cubical’ cells, is homotopy equivalent to the free loop space ΛY and the differential graded module of chains C∗(Λ̂X) generalizes the coHochschild chain complex of the chain coalgebra C*(X).
