Basu, Samik; Blanc, David; Sen, Debasis Note on Toda brackets. (English) Zbl 1460.55016 J. Homotopy Relat. Struct. 15, No. 3-4, 495-510 (2020). Toda brackets, defined by H. Toda [J. Inst. Polytechn., Osaka City Univ., Ser. A 3, 43–82 (1952; Zbl 0049.12903)], play an important role in homotopy theory both for their original purpose of calculating homotopy groups, and because they serve as differentials in spectral sequences. The notion has been generalized in several ways, e.g., in [H.-J. Baues et al., J. Homotopy Relat. Struct. 11, No. 4, 643–677 (2016; Zbl 1360.18026)] and [G. Walker, in: Proc. adv. Study Inst. algebraic Topol.various Publ. Ser. 13, 612–631 (1970; Zbl 0224.55023)]. The authors provide a definition of higher Toda brackets in a general pointed model category \(\mathcal{C}\), show how these appear as the successive obstructions to strictifying certain diagrams (namely, chain complexes in the homotopy category \(\mathrm{ho}\,\mathcal{C}\)), explain the connection with the traditional stable description in terms of filtered complexes and provide two examples of settings in which higher Toda brackets occur. Reviewer: Marek Golasiński (Olsztyn) Cited in 4 Documents MSC: 55Q35 Operations in homotopy groups 55P99 Homotopy theory 55Q40 Homotopy groups of spheres Keywords:higher homotopy operations; Toda brackets; stable homotopy Citations:Zbl 0049.12903; Zbl 1360.18026; Zbl 0224.55023 PDFBibTeX XMLCite \textit{S. Basu} et al., J. Homotopy Relat. Struct. 15, No. 3--4, 495--510 (2020; Zbl 1460.55016) Full Text: DOI arXiv References: [1] Adams, JF, On the non-existence of elements of Hopf invariant one, Ann. Math. 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