Kalelkar, Tejas Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds. (English) Zbl 1446.57012 Proc. Am. Math. Soc. 148, No. 10, 4527-4529 (2020). Summary: T. H. Colding and D. Gabai [Duke Math. J. 167, No. 15, 2793–2832 (2018; Zbl 1403.57012)] have given an effective version of T. Li’s theorem [J. Am. Math. Soc. 19, No. 3, 625–657 (2006; Zbl 1108.57015)] that non-Haken hyperbolic 3-manifolds have finitely many irreducible Heegaard splittings. As a corollary of their work, we show that Haken hyperbolic 3-manifolds have a finite collection of strongly irreducible Heegaard surfaces \(S_i\) and incompressible surfaces \(K_j\) such that any strongly irreducible Heegaard surface is a Haken sum \(S_i+\sum_jn_jK_j\), up to one-sided associates of the Heegaard surfaces. MSC: 57K30 General topology of 3-manifolds 57K32 Hyperbolic 3-manifolds 57M50 General geometric structures on low-dimensional manifolds 57M99 General low-dimensional topology Citations:Zbl 1403.57012; Zbl 1108.57015 PDFBibTeX XMLCite \textit{T. Kalelkar}, Proc. Am. Math. Soc. 148, No. 10, 4527--4529 (2020; Zbl 1446.57012) Full Text: DOI arXiv References: [1] Colding, Tobias Holck; Gabai, David, Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds, Duke Math. J., 167, 15, 2793-2832 (2018) · Zbl 1403.57012 · doi:10.1215/00127094-2018-0022 [2] Li, Tao, Heegaard surfaces and measured laminations. II. Non-Haken 3-manifolds, J. Amer. Math. Soc., 19, 3, 625-657 (2006) · Zbl 1108.57015 · doi:10.1090/S0894-0347-06-00520-0 [3] Moriah, Yoav; Schleimer, Saul; Sedgwick, Eric, Heegaard splittings of the form \(H+nK\), Comm. Anal. Geom., 14, 2, 215-247 (2006) · Zbl 1119.57008 [4] Oertel, U., Incompressible branched surfaces, Invent. Math., 76, 3, 385-410 (1984) · Zbl 0539.57006 · doi:10.1007/BF01388466 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.