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arXiv · 2610.38760

On a Conjecture of Fiedorowicz

Oren Ben-Bassat
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Abstract

Fiedorowicz conjectured that every finite simply connected CW complex is homotopy equivalent to the classifying space of a finite monoid. We prove this conjecture. Our main construction takes a finite monoid M and a map from a finite connected CW complex into the classifying space of M, and produces a new finite monoid whose classifying space is homotopy equivalent to the mapping cone of the given map. Applying this construction successively to the attaching maps of a finite CW model proves the result. As an explicit example of the algorithm, we construct a 1795-element monoid whose classifying space is homotopy equivalent to two dimensional complex projective space.

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Oren Ben-Bassat. 2026-10-28. On a Conjecture of Fiedorowicz. https://arxiv.org/abs/2610.38760

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