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On keen weakly reducible bridge spheres

Puttipong Pongtanapaisan and Daniel Rodman

Algebraic & Geometric Topology 24 (2024) 4201–4235
Bibliography
1 D Bachman, Topological index theory for surfaces in 3–manifolds, Geom. Topol. 14 (2010) 585 MR2602846
2 D Bachman, Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3–manifolds, Math. Ann. 355 (2013) 697 MR3010144
3 D Bachman, J Johnson, On the existence of high index topologically minimal surfaces, Math. Res. Lett. 17 (2010) 389 MR2653676
4 M Campisi, M Rathbun, Hyperbolic manifolds containing high topological index surfaces, Pacific J. Math. 296 (2018) 305 MR3830837
5 M Campisi, L Torres, The disk complex and topologically minimal surfaces in the 3–sphere, J. Knot Theory Ramifications 29 (2020) 2050092 MR4216036
6 S Cho, Homeomorphisms of the 3–sphere that preserve a Heegaard splitting of genus two, Proc. Amer. Math. Soc. 136 (2008) 1113 MR2361888
7 Q E, On keen weakly reducible Heegaard splittings, Topology Appl. 231 (2017) 128 MR3712959
8 Q E, F Lei, Topologically minimal surfaces versus self-amalgamated Heegaard surfaces, Sci. China Math. 57 (2014) 2393 MR3266499
9 Q E, Z Zhang, On Heegaard splittings with finitely many pairs of disjoint compression disks, J. Math. Res. Appl. 43 (2023) 496 MR4615811
10 M Freedman, J Hass, P Scott, Least area incompressible surfaces in 3–manifolds, Invent. Math. 71 (1983) 609 MR695910
11 J Johnson, Mapping class groups of Heegaard splittings of surface bundles, preprint (2012) arXiv:1201.2628
12 J Johnson, Y Moriah, Bridge distance and plat projections, Algebr. Geom. Topol. 16 (2016) 3361 MR3584261
13 D Ketover, Y Liokumovich, A Song, On the existence of minimal Heegaard surfaces, preprint (2019) arXiv:1911.07161
14 J Kim, A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical, Algebr. Geom. Topol. 16 (2016) 1427 MR3523045
15 J H Lee, On topologically minimal surfaces of high genus, Proc. Amer. Math. Soc. 143 (2015) 2725 MR3326050
16 J H Lee, Bridge spheres for the unknot are topologically minimal, Pacific J. Math. 282 (2016) 437 MR3478944
17 L Liang, F Li, J Li, Reducible handle additions to weakly reducible Heegaard splittings, Topology Appl. 242 (2018) 33 MR3802171
18 D McCullough, Virtually geometrically finite mapping class groups of 3–manifolds, J. Differential Geom. 33 (1991) 1 MR1085134
19 Y Moriah, Heegaard splittings of knot exteriors, from: "Workshop on Heegaard splittings", Geom. Topol. Monogr. 12, Geom. Topol. Publ. (2007) 191 MR2408247
20 J P Otal, Presentations en ponts des nœuds rationnels, from: "Low-dimensional topology", Lond. Math. Soc. Lect. Note Ser. 95, Cambridge Univ. Press (1985) 143 MR827300
21 M Ozawa, Nonminimal bridge positions of torus knots are stabilized, Math. Proc. Cambridge Philos. Soc. 151 (2011) 307 MR2823138
22 D Rodman, An infinite family of links with critical bridge spheres, Algebr. Geom. Topol. 18 (2018) 153 MR3748241
23 M Scharlemann, Thin position in the theory of classical knots, from: "Handbook of knot theory", Elsevier (2005) 429 MR2179267
24 J Schultens, Width complexes for knots and 3–manifolds, Pacific J. Math. 239 (2009) 135 MR2449015
25 F Urbano, Minimal surfaces with low index in the three-dimensional sphere, Proc. Amer. Math. Soc. 108 (1990) 989 MR1007516
26 A Zupan, Properties of knots preserved by cabling, Comm. Anal. Geom. 19 (2011) 541 MR2843241