A combinatorial model for the free loop fibration

Manuel Rivera, Samson Saneblidze

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We introduce the abstract 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 ΛX such that its geometric realization |ΛX|, 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*(ΛX) generalizes the coHochschild chain complex of the chain coalgebra C*(X).

Original languageEnglish (US)
Pages (from-to)1085-1101
Number of pages17
JournalBulletin of the London Mathematical Society
Issue number6
StatePublished - Dec 2018


  • 18F20 (primary)
  • 52B05
  • 55P35
  • 55U05

ASJC Scopus subject areas

  • Mathematics(all)


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