### 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 language | English (US) |
---|---|

Pages (from-to) | 1085-1101 |

Number of pages | 17 |

Journal | Bulletin of the London Mathematical Society |

Volume | 50 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2018 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the London Mathematical Society*,

*50*(6), 1085-1101. https://doi.org/10.1112/blms.12202

**A combinatorial model for the free loop fibration.** / Rivera, Manuel; Saneblidze, Samson.

Research output: Contribution to journal › Article

*Bulletin of the London Mathematical Society*, vol. 50, no. 6, pp. 1085-1101. https://doi.org/10.1112/blms.12202

}

TY - JOUR

T1 - A combinatorial model for the free loop fibration

AU - Rivera, Manuel

AU - Saneblidze, Samson

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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).

AB - 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).

KW - 18F20 (primary)

KW - 52B05

KW - 55P35

KW - 55U05

UR - http://www.scopus.com/inward/record.url?scp=85052831265&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052831265&partnerID=8YFLogxK

U2 - 10.1112/blms.12202

DO - 10.1112/blms.12202

M3 - Article

VL - 50

SP - 1085

EP - 1101

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 6

ER -