New Bounds on Distributional Sectional Category and Applications to Distributional Homotopic Distance
Abstract
In this paper, we establish several new bounds for the distributional sectional category (dsecat). We first prove Jauhari's conjecture, thereby establishing a cohomological lower bound for dsecat with arbitrary coefficients. We then obtain an analogous lower bound with rational coefficients by constructing a natural graded ℚ-linear section of the homomorphism induced in cohomology by the symmetric diagonal. As applications, we provide several computations of the distributional sectional category. We also establish multiplicative product and composition inequalities for dsecat. Finally, we apply these results to distributional homotopic distance. A sequential version of this invariant was recently introduced by Jauhari and Oprea; we give an equivalent formulation in terms of distributed homotopies and derive new fibration and multiplicative triangle inequalities.
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BibTeX
@misc{daundkar2026bounds,
title = {{New Bounds on Distributional Sectional Category and Applications to Distributional Homotopic Distance}},
author = {Navnath Daundkar and J. M. García-Calcines},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.08298},
eprint = {2608.08298},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08298},
}
RIS
TY - UNPB
TI - New Bounds on Distributional Sectional Category and Applications to Distributional Homotopic Distance
AU - Navnath Daundkar
AU - J. M. García-Calcines
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2608.08298
UR - https://arxiv.org/abs/2608.08298
AB - In this paper, we establish several new bounds for the distributional sectional category (dsecat). We first prove Jauhari's conjecture, thereby establishing a cohomological lower bound for dsecat with arbitrary coefficients. We then obtain an analogous lower bound with rational coefficients by constructing a natural graded ℚ-linear section of the homomorphism induced in cohomology by the symmetric diagonal. As applications, we provide several computations of the distributional sectional category. We also establish multiplicative product and composition inequalities for dsecat. Finally, we apply these results to distributional homotopic distance. A sequential version of this invariant was recently introduced by Jauhari and Oprea; we give an equivalent formulation in terms of distributed homotopies and derive new fibration and multiplicative triangle inequalities.
ER -