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Algebraically and geometrically minimal DG-models of diagrams of spaces
Abstract
We extend Sullivan's rational homotopy theory by constructing geometrically and algebraically minimal models for diagrams of simply connected spaces over a class of finite indexing categories. Both classes classify rational diagram homotopy types, but their minimality conditions can differ. We also show that, in contrast to classical rational homotopy theory, H-diagrams need not split into products of Eilenberg--MacLane diagrams, and characterize the indexing categories for which every H-diagram admits such a splitting. Also we apply this to computation of automorphism groups of rational homotopy types of certain diagrams of spaces.
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BibTeX
@misc{golub2026algebraically,
title = {{Algebraically and geometrically minimal DG-models of diagrams of spaces}},
author = {Nikita Golub},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34822},
eprint = {2609.34822},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34822},
}
RIS
TY - UNPB
TI - Algebraically and geometrically minimal DG-models of diagrams of spaces
AU - Nikita Golub
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34822
UR - https://arxiv.org/abs/2609.34822
AB - We extend Sullivan's rational homotopy theory by constructing geometrically and algebraically minimal models for diagrams of simply connected spaces over a class of finite indexing categories. Both classes classify rational diagram homotopy types, but their minimality conditions can differ. We also show that, in contrast to classical rational homotopy theory, H-diagrams need not split into products of Eilenberg--MacLane diagrams, and characterize the indexing categories for which every H-diagram admits such a splitting. Also we apply this to computation of automorphism groups of rational homotopy types of certain diagrams of spaces.
ER -