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Uniqueness of differential Poincaré duality models
Abstract
We prove the remaining even-dimensional case of the Lambrechts--Stanley "uniqueness" conjecture for 1-connected differential Poincaré duality models. Together with our previous odd-dimensional result, this shows that any two such algebras weakly homotopy equivalent as PDGAs admit direct PDGA quasi-isomorphisms into a common connected differential Poincaré duality algebra. We use our previous method of obtaining differential Poincaré duality models as nondegenerate quotients of Hodge extensions, the new ingredient being a Hodge extension in the middle degree.
Related
BibTeX
@misc{hajek2026uniqueness,
title = {{Uniqueness of differential Poincaré duality models}},
author = {Pavel Hájek},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14221},
eprint = {2609.14221},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14221},
}
RIS
TY - UNPB
TI - Uniqueness of differential Poincaré duality models
AU - Pavel Hájek
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14221
UR - https://arxiv.org/abs/2609.14221
AB - We prove the remaining even-dimensional case of the Lambrechts--Stanley "uniqueness" conjecture for 1-connected differential Poincaré duality models. Together with our previous odd-dimensional result, this shows that any two such algebras weakly homotopy equivalent as PDGAs admit direct PDGA quasi-isomorphisms into a common connected differential Poincaré duality algebra. We use our previous method of obtaining differential Poincaré duality models as nondegenerate quotients of Hodge extensions, the new ingredient being a Hodge extension in the middle degree.
ER -