Homotopy exponents for large H-spaces

TL;DR

This paper proves that H-spaces with finitely generated cohomology have homotopy exponents at all primes, answering a longstanding question in algebraic topology.

Contribution

It establishes the existence of homotopy exponents for a broad class of H-spaces with finitely generated cohomology, extending previous results.

Findings

H-spaces with finitely generated cohomology have homotopy exponents at all primes

Provides a positive answer to Stanley's question

Extends understanding of the structure of large H-spaces

Abstract

We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.