Topological complexity of $S^3/Q_8$ as fibrewise L-S category - Collections | Kyushu University Library

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＜journal article＞
Topological complexity of $S^3/Q_8$ as fibrewise L-S category

Creator	Author PID K000528 0009-0007-3137-168X Creator Name Iwase, Norio 岩瀬, 則夫イワセ, ノリオ Affiliation Affiliation Name Faculty of Mathematics, Kyushu University 九州大学大学院数理学研究院
Creator	Author PID 0000-0002-8114-1803 Creator Name Miyata, Yuya 宮田, 祐也ミヤタ, ユウヤ Affiliation Affiliation Name Graduate School of Mathematics, Kyushu University 九州大学大学院数理学府数理学専攻
Language	English
Publisher	Juliusz Schauder University Center for Nonlinear Studies
Date	2023-09-23
Source Title	Topological methods in nonlinear analysis
Publication Type	Accepted Manuscript
Access Rights	embargoed access
Date of Available	2024-09-23
Related DOI	isVersionOf https://doi.org/10.12775/TMNA.2022.068

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Published Date：2024.09.23	pdf	211 KB

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PISSN	1230-3429
NCID	AA11059678
Record ID	6796418
Subject Terms	Topological complexity
	space form
	quaternion group
	python program
Notes	In 2010, M. Sakai and the first author showed that the topological complexity of a space $X$ coincides with the fibrewise unpointed L-S category of a pointed fibrewise space $＼proj_{1} ＼colon X ＼times X ＼to X$ with the diagonal map $＼Delta ＼colon X ＼to X ＼times X$ as its section. In this paper, we describe our algorithm how to determine the fibrewise L-S category or the Topological Complexity of a topological spherical space form. Especially, for $S^3/Q_8$ where $Q_8$ is the quaternion group, we write a python code to realise the algorithm to determine its Topological Complexity.
	[Alternative abstract Notation]In 2010, M. Sakai and the first author showed that the topological complexity of a space 𝑋 coincides with the fibrewise unpointed L-S category of a pointed fibrewise space pr_1 ∶ 𝑋 × 𝑋 → 𝑋 with the diagonal map Δ ∶ 𝑋 → 𝑋 × 𝑋 as its section. In this paper, we describe our algorithm how to determine the fibrewise L-S category or the Topological Complexity of a topological spherical space form. Especially, for 𝑆^3∕_𝑄8 where 𝑄_8 is the quaternion group, we write a python code to realise the algorithm to determine its Topological Complexity.
	2020 Mathematics Subject Classification. Primary: 55M30; Secondary: 55R70, 55M35, 55P35, 57T30.
Type	Articles
Funding Information	Funder Name Japan Society for the Promotion of Science (JSPS) 日本学術振興会 Award Number 17H06128 Award Title Innovative research of geometric topology and singularities of differentiable mappings 幾何的トポロジーと写像の特異点論の革新的研究
	Funder Name Japan Society for the Promotion of Science (JSPS) 日本学術振興会 Award Number 18K18713 Award Title Building-up Differential Homotopy Theory 微分ホモトピー論の構築
	Funder Name Japan Society for the Promotion of Science (JSPS) 日本学術振興会 Award Number 23K03093 Award Title Topological Complexity and A-infinity structure 位相的複雑さとＡ∞構造
Created Date	2023.09.25
Modified Date	2023.09.26