### Abstract

We define and study a certain class of spaces which includes p-completed classifying spaces of compact Lie groups, classifying spaces of p-compact groups, and p completed classifying spaces of certain locally finite discrete groups. These spaces are determined by fusion and linking systems over "discrete p-toral groups" - extensions of (Z/p(infinity))(r) by finite p-groups - in the same way that classifying spaces of p-local finite groups as defined in our paper [ 7] are determined by fusion and linking systems over finite p - groups. We call these structures "p-local compact groups".

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

Pages (from-to) | 315-427 |

Number of pages | 113 |

Journal | Geometry & Topology |

Volume | 11 |

DOIs | |

Publication status | Published - 2007 |

### Keywords

- classifying-spaces
- self-maps
- classification
- equivalences
- fusion
- limits
- BG

### Cite this

*Geometry & Topology*,

*11*, 315-427. https://doi.org/10.2140/GT.2007.11.315

**Discrete models for the p-local homotopy theory of compact Lie groups and p-compact groups.** / Broto, Carles; Levi, Ran; Oliver, Bob.

Research output: Contribution to journal › Article

*Geometry & Topology*, vol. 11, pp. 315-427. https://doi.org/10.2140/GT.2007.11.315

}

TY - JOUR

T1 - Discrete models for the p-local homotopy theory of compact Lie groups and p-compact groups

AU - Broto, Carles

AU - Levi, Ran

AU - Oliver, Bob

PY - 2007

Y1 - 2007

N2 - We define and study a certain class of spaces which includes p-completed classifying spaces of compact Lie groups, classifying spaces of p-compact groups, and p completed classifying spaces of certain locally finite discrete groups. These spaces are determined by fusion and linking systems over "discrete p-toral groups" - extensions of (Z/p(infinity))(r) by finite p-groups - in the same way that classifying spaces of p-local finite groups as defined in our paper [ 7] are determined by fusion and linking systems over finite p - groups. We call these structures "p-local compact groups".

AB - We define and study a certain class of spaces which includes p-completed classifying spaces of compact Lie groups, classifying spaces of p-compact groups, and p completed classifying spaces of certain locally finite discrete groups. These spaces are determined by fusion and linking systems over "discrete p-toral groups" - extensions of (Z/p(infinity))(r) by finite p-groups - in the same way that classifying spaces of p-local finite groups as defined in our paper [ 7] are determined by fusion and linking systems over finite p - groups. We call these structures "p-local compact groups".

KW - classifying-spaces

KW - self-maps

KW - classification

KW - equivalences

KW - fusion

KW - limits

KW - BG

U2 - 10.2140/GT.2007.11.315

DO - 10.2140/GT.2007.11.315

M3 - Article

VL - 11

SP - 315

EP - 427

JO - Geometry & Topology

JF - Geometry & Topology

SN - 1364-0380

ER -