Title: A combinatorial model for the free loop fibration,
Abstract: We introduce the abstract notion of a closed necklical set in order to
describe a functorial combinatorial model of the free loop fibration $\Omega
Y\rightarrow \Lambda Y\rightarrow Y$ 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
$\widehat{\mathbf{\Lambda}}X$ such that its geometric realization
$|\widehat{\mathbf{\Lambda}}X|$, a space built out of gluing "freehedrical" and
"cubical" cells, is homotopy equivalent to the free loop space $\Lambda Y$ and
the differential graded module of chains $C_*(\widehat{\mathbf{\Lambda}}X)$
generalizes the coHochschild chain complex of the chain coalgebra $C_\ast(X).$