Correction to ""Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology"

TL;DR

This paper provides a correction to a previous work on topological nonrealization results, addressing a gap in the proof of a key corollary and ensuring the validity of the main theorem and examples.

Contribution

The authors clarify and complete the proof of their main theorem regarding topological nonrealization, correcting an earlier oversight in their 2008 paper.

Findings

Correction of the proof of Corollary 4.5

Validation of the main theorem and examples from the original paper

Abstract

Manfred Stelzer has pointed out that part of Corollary 4.5 of our paper "Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology" [Alg. Geo. Top. 8 (2008), 2109--2129] was not sufficiently proved, and, indeed, is likely incorrect as stated. This necessitates a little more argument to finish the proof of the main theorem of the original paper. The statement of this theorem, and all the examples, remain unchanged.