PreprintCC BY 4.0arXiv
On a Conjecture of Fiedorowicz
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.
Related
BibTeX
@misc{benbassat2026conjecture,
title = {{On a Conjecture of Fiedorowicz}},
author = {Oren Ben-Bassat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38760},
eprint = {2610.38760},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38760},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On a Conjecture of Fiedorowicz
AU - Oren Ben-Bassat
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38760
UR - https://arxiv.org/abs/2610.38760
AB - 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.
ER -