An Algebraic Model for Finite Loop Spaces

Carles Broto, Ran Levi, Bob Oliver

Research output: Contribution to journalArticle

7 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

Keywords

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

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