An Algebraic Model for Finite Loop Spaces

Carles Broto, Ran Levi, Bob Oliver

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)2915-2982
Number of pages67
JournalAlgebraic & Geometric Topology
Volume14
DOIs
Publication statusPublished - 5 Nov 2014

Fingerprint

Loop Space
Compact Group
Classifying Space
P-groups
Homotopy
Linking
Fusion
Model
Cover
Imply

Keywords

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

Cite this

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

In: Algebraic & Geometric Topology, Vol. 14, 05.11.2014, p. 2915-2982.

Research output: Contribution to journalArticle

Broto, Carles ; Levi, Ran ; Oliver, Bob. / An Algebraic Model for Finite Loop Spaces. In: Algebraic & Geometric Topology. 2014 ; Vol. 14. pp. 2915-2982.
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