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On the sequential topological complexity of group homomorphisms (2402.13389v1)
Published 20 Feb 2024 in math.AT and math.GR
Abstract: We define and develop a homotopy invariant notion for the sequential topological complexity of a map $f:X\to Y,$ denoted $TC_{r}(f)$, that interacts with $TC_{r}(X)$ and $TC_{r}(Y)$ in the same way Jamie Scott's topological complexity map $TC(f)$ interacts with $TC(X)$ and $TC(Y).$ Furthermore, we apply $TC_{r}(f)$ to studying group homomorphisms $\phi: \Gamma\to \Lambda.$ In addition, we prove that the sequential topological complexity of any nonzero homomorphism of a torsion group cannot be finite. Also, we give the characterisation of cohomological dimension of group homomorphisms.
- Berstein–Schwarz, On the Lusternik-Schnirelmann category of Grassmannians. Math. Proc. Camb. Philos. Soc. 79 (1976) 129-134.
- Lusternik-Schnirelmann Category, AMS, 2003.
- M. Grant, https://mathoverflow.net/questions/89178/cohomological-dimension-of𝑓fitalic_f-a-homomorphism
- E. Jauhari. “On Sequential Versions of Distributional Topological Complexity.” preprint, arXiv:2401.15667 [math.AT] (2024), 27 pp.
- L. Lusternik, L. Schnirelmann, “Sur le probleme de trois geodesiques fermees sur les surfaces de genre 0”, Comptes Rendus de l’Academie des Sciences de Paris, 189: (1929) 269-271.
- Murillo A, Wu J. Topological complexity of the work map. Journal of Topology and Analysis 2021; 13 (01): 219-238.
- Yu. Rudyak On higher analogs of topological complexity. Topology and its Applications 2010; 157 (5): 916-920. Erratum in Topology and its Applications 2010; 157 (6): 1118.
- Yu. Rudyak, S. Soumen. Relative LS categories and higher topological complexities of maps. Topology and its Applications 2022; 322: 108317.
- C. ZAPATA, J. GONZÁLEZ.“Higher topological complexity of a map,” Turkish Journal of Mathematics: (2023) Vol. 47: No. 6, Article 3. https://doi.org/10.55730/1300-0098.3453;
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