Title: A combinatorial model for the path fibration,
Abstract: We introduce the abstract notion of a necklical set in order to describe a
functorial combinatorial model of the path fibration over the geometric
realization of a path connected simplicial set. In particular, to any path
connected simplicial set $X$ we associate a necklical set
$\widehat{\mathbf{\Omega}}X$ such that its geometric realization
$|\widehat{\mathbf{\Omega}}X|$, a space built out of gluing cubical cells, is
homotopy equivalent to the based loop space on $|X|$ and the differential
graded module of chains $C_*(\widehat{\mathbf{\Omega}}X)$ is a differential
graded associative algebra generalizing Adams' cobar construction.