Equivariant and invariant parametrized topological complexity

[2412.12921] Equivariant and invariant parametrized topological complexity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Topology arXiv:2412.12921 (math) [Submitted on 17 Dec 2024 ( v1 ), last revised 20 Apr 2026 (this version, v5)] Title: Equivariant and invariant parametrized topological complexity Authors: Ramandeep Singh Arora , Navnath Daundkar View a PDF of the paper titled Equivariant and invariant parametrized topological complexity, by Ramandeep Singh Arora and 1 other authors View PDF HTML (experimental) Abstract: For a $G$-equivariant fibration $p \colon E\to B$, we introduce and study the invariant analogue of Cohen, Farber and Weinberger's parametrized topological complexity, called the invariant parametrized topological complexity. This notion generalizes the invariant topological complexity introduced by Lubawski and Marzantowicz. When $G$ is a compact Lie group acting freely on $E$, we show that the invariant parametrized topological complexity of the $G$-fibration $p \colon E\to B$ coincides with the parametrized topological complexity of the induced fibration $\overline{p} \colon \overline{E} \to \overline{B}$ between the orbit spaces. Furthermore, we compute the invariant parametrized topological complexity of equivariant Fadell-Neuwirth fibrations, which measures the complexity of motion planning in the presence of obstacles with unknown positions, where the order of their placement is irrelevant. In addition, we study the equivariant sectional category and the equivariant parametrized topological complexity, which serve as essential tools for obtaining several results in this paper. Comments: 37 pages. This is the final version that will appear in the journal Proceedings of the Royal Society of Edinburgh: Section A Mathematics Subjects: Algebraic Topology (math.AT) MSC classes: 55M30, 55R91, 55S40 Cite as: arXiv:2412.12921 [math.AT] (or arXiv:2412.12921v5 [math.AT] for this version) https://doi.org/10.48550/arXiv.2412.12921 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1017/prm.2026.10147 Focus to learn more DOI(s) linking to related resources Submission history From: Ramandeep Singh Arora [ view email ] [v1] Tue, 17 Dec 2024 13:53:58 UTC (27 KB) [v2] Wed, 12 Mar 2025 09:40:40 UTC (35 KB) [v3] Thu, 29 May 2025 12:10:26 UTC (43 KB) [v4] Mon, 1 Dec 2025 11:17:41 UTC (56 KB) [v5] Mon, 20 Apr 2026 16:54:15 UTC (57 KB) Full-text links: Access Paper: View a PDF of the paper titled Equivariant and invariant parametrized topological complexity, by Ramandeep Singh Arora and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AT < prev | next > new | recent | 2024-12 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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