2024 Sectional category of maps related to finite spaces
Kohei Tanaka
Topol. Methods Nonlinear Anal. Advance Publication 1-21 (2024). DOI: 10.12775/TMNA.2023.029

Abstract

In this study, we compute some examples of sectional category secat$(f)$ and sectional number sec$(f)$ for continuous maps $f$ related to finite spaces. Moreover, we introduce an invariant secat$_k(f)$ for a map $f$ between finite spaces using the $k$-th barycentric subdivision and show the equality secat$_k(f)=$ secat$(\mathcal{B}(f))$ for sufficiently large $k$, where $\mathcal{B}(f)$ is the induced map on the associated polyhedra.

Citation

Download Citation

Kohei Tanaka. "Sectional category of maps related to finite spaces." Topol. Methods Nonlinear Anal. Advance Publication 1 - 21, 2024. https://doi.org/10.12775/TMNA.2023.029

Information

Published: 2024
First available in Project Euclid: 16 March 2024

Digital Object Identifier: 10.12775/TMNA.2023.029

Keywords: finite space , fixed point , Lusternik-Schnirelmann category , poset , sectional category

Rights: Copyright © 2024 Juliusz P. Schauder Centre for Nonlinear Studies

JOURNAL ARTICLE
21 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Back to Top