Correction to: An algebraic model for finite loop spaces

TL;DR

This note corrects two errors in BLO6 by proving that the inclusion of linking systems along a single $\mathcal{F}$-conjugacy class preserves the homotopy type of nerves, and by establishing a Lambda-functor framework for transporter systems to compare cohomological invariants across conjugate objects. The arguments rely on Quillen's Theorem A, the bullet construction, and transporter-system machinery to ensure stability of the homotopy type and of $\Lambda^*(G;M)$ under conjugation within $P^{\mathcal{F}}$. These corrections refine the algebraic model for finite loop spaces and clarify how fusion data are encoded by linking and transporter systems. Together, they strengthen the foundations for using fusion-system techniques in the study of $p$-local classifying spaces.

Abstract

We correct here two errors in our earlier paper "An algebraic model for finite loop spaces" [arXiv:1212.2033]

Theorems & Definitions (16)

• Proposition 1.1
• proof
• Lemma 1.2
• proof
• Definition 1.3: BLO3
• Proposition 1.4: BLO3
• proof
• Lemma 1.5
• proof
• Proposition 1.6