A combinatorial model for the path fibration

Manuel Rivera, Samson Saneblidze

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 Ω^ X such that its geometric realization | Ω^ 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 (Ω^ X) is a differential graded associative algebra generalizing Adams’ cobar construction.

Original languageEnglish (US)
Pages (from-to)393-410
Number of pages18
JournalJournal of Homotopy and Related Structures
Issue number2
StatePublished - Jun 11 2019

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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