PreprintCC BY-NC-ND 4.0arXiv
Sectional category versus module sectional category for retractive maps
Abstract
We construct a map between simply connected rational spaces of finite rational type which admits a homotopy retraction and satisfies msecat(p)=2<secat(p)=3. The target is the rationalization of a simply connected twelve-dimensional CW complex with eleven cells, and is rationally hyperbolic. This disproves Carrasquel--Vera's conjecture for retractive maps.
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BibTeX
@misc{parent2026sectional,
title = {{Sectional category versus module sectional category for retractive maps}},
author = {Paul-Eugene Parent},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00089},
eprint = {2610.00089},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00089},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Sectional category versus module sectional category for retractive maps
AU - Paul-Eugene Parent
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00089
UR - https://arxiv.org/abs/2610.00089
AB - We construct a map between simply connected rational spaces of finite rational type which admits a homotopy retraction and satisfies msecat(p)=2<secat(p)=3. The target is the rationalization of a simply connected twelve-dimensional CW complex with eleven cells, and is rationally hyperbolic. This disproves Carrasquel--Vera's conjecture for retractive maps.
ER -