2017/06/03 by Rivera, Manuel, Saneblidze, Samson
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.00983
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\mathbfΩX such that its geometric realization |\widehat\mathbfΩX|, 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\mathbfΩX) is a differential graded associative algebra generalizing Adams' cobar construction.