### Abstract

Original language | English |
---|---|

Pages (from-to) | 2915-2982 |

Number of pages | 67 |

Journal | Algebraic & Geometric Topology |

Volume | 14 |

DOIs | |

Publication status | Published - 5 Nov 2014 |

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### Keywords

- finite loop spaces
- classifying spaces
- p–local compact groups
- fusion

### Cite this

*Algebraic & Geometric Topology*,

*14*, 2915-2982. https://doi.org/10.2140/agt.2014.14.2915

**An Algebraic Model for Finite Loop Spaces.** / Broto, Carles; Levi, Ran; Oliver, Bob.

Research output: Contribution to journal › Article

*Algebraic & Geometric Topology*, vol. 14, pp. 2915-2982. https://doi.org/10.2140/agt.2014.14.2915

}

TY - JOUR

T1 - An Algebraic Model for Finite Loop Spaces

AU - Broto, Carles

AU - Levi, Ran

AU - Oliver, Bob

PY - 2014/11/5

Y1 - 2014/11/5

N2 - A p-local compact group consists of a discrete p-toral group S, together with a fusion system and a linking system over S which define a classifying space having very nice homotopy properties. We prove here that if some finite regular cover of a space Y is the classifying space of a p-local compact group, then so is Y^p . Together with earlier results by Dwyer and Wilkerson and by the authors, this implies as a special case that a finite loop space determines a p-local compact group at each prime p.

AB - A p-local compact group consists of a discrete p-toral group S, together with a fusion system and a linking system over S which define a classifying space having very nice homotopy properties. We prove here that if some finite regular cover of a space Y is the classifying space of a p-local compact group, then so is Y^p . Together with earlier results by Dwyer and Wilkerson and by the authors, this implies as a special case that a finite loop space determines a p-local compact group at each prime p.

KW - finite loop spaces

KW - classifying spaces

KW - p–local compact groups

KW - fusion

U2 - 10.2140/agt.2014.14.2915

DO - 10.2140/agt.2014.14.2915

M3 - Article

VL - 14

SP - 2915

EP - 2982

JO - Algebraic & Geometric Topology

JF - Algebraic & Geometric Topology

SN - 1472-2747

ER -