A combinatorial model for the free loop fibration

Manuel Rivera, Samson Saneblidze

Research output: Contribution to journalArticle

Abstract

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
Volume50
Issue number6
DOIs
StatePublished - Dec 1 2018

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'A combinatorial model for the free loop fibration'. Together they form a unique fingerprint.

Cite this