### Abstract

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.

Original language | English |
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Pages (from-to) | 2915-2982 |

Number of pages | 67 |

Journal | Algebraic & Geometric Topology |

Volume | 14 |

DOIs | |

Publication status | Published - 5 Nov 2014 |

### Keywords

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

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## Profiles

### Ran Levi

- Mathematical Sciences (Research Theme)
- School of Natural & Computing Sciences, Mathematical Science - Chair in Mathematical Sciences

Person: Academic

## Cite this

Broto, C., Levi, R., & Oliver, B. (2014). An Algebraic Model for Finite Loop Spaces.

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