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An algorithm to determine the Heegaard genus of a $3$–manifold

Tao Li

Geometry & Topology 15 (2011) 1029–1106
Bibliography
1 I Agol, T Li, An algorithm to detect laminar $3$–manifolds, Geom. Topol. 7 (2003) 287 MR1988287
2 M Boileau, D J Collins, H Zieschang, Genus $2$ Heegaard decompositions of small Seifert manifolds, Ann. Inst. Fourier (Grenoble) 41 (1991) 1005 MR1150575
3 F Bonahon, J P Otal, Scindements de Heegaard des espaces lenticulaires, Ann. Sci. École Norm. Sup. $(4)$ 16 (1983) MR740078
4 A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275 MR918537
5 W Floyd, U Oertel, Incompressible surfaces via branched surfaces, Topology 23 (1984) 117 MR721458
6 W Haken, Theorie der Normalflächen, Acta Math. 105 (1961) 245 MR0141106
7 W Jaco, U Oertel, An algorithm to decide if a $3$–manifold is a Haken manifold, Topology 23 (1984) 195 MR744850
8 W Jaco, J H Rubinstein, $0$–efficient triangulations of $3$–manifolds, J. Differential Geom. 65 (2003) 61 MR2057531
9 K Johannson, Heegaard surfaces in Haken $3$–manifolds, Bull. Amer. Math. Soc. $($N.S.$)$ 23 (1990) 91 MR1027902
10 K Johannson, Topology and combinatorics of $3$–manifolds, Lecture Notes in Math. 1599, Springer (1995) MR1439249
11 H Kneser, Geschlossene Flachen in Dreidimensionalen Mannigfaltigkeiten, Jahres. der Deut. Math. Verein. 38 (1929) 248
12 T Li, Laminar branched surfaces in $3$–manifolds, Geom. Topol. 6 (2002) 153 MR1914567
13 T Li, Heegaard surfaces and measured laminations. II: Non-Haken $3$_-manifolds, J. Amer. Math. Soc. 19 (2006) 625 MR2220101
14 T Li, Heegaard surfaces and measured laminations. I: The Waldhausen conjecture, Invent. Math. 167 (2007) 135 MR2264807
15 Y Moriah, Heegaard splittings of Seifert fibered spaces, Invent. Math. 91 (1988) 465 MR928492
16 U Oertel, Incompressible branched surfaces, Invent. Math. 76 (1984) 385 MR746535
17 U Oertel, Measured laminations in $3$–manifolds, Trans. Amer. Math. Soc. 305 (1988) 531 MR924769
18 J H Rubinstein, Polyhedral minimal surfaces, Heegaard splittings and decision problems for $3$–dimensional manifolds, from: "Geometric topology (Athens, GA, 1993)" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1 MR1470718
19 M Scharlemann, Local detection of strongly irreducible Heegaard splittings, Topology Appl. 90 (1998) 135 MR1648310
20 M Scharlemann, A Thompson, Thin position for $3$–manifolds, from: "Geometric topology (Haifa, 1992)" (editors C M Gordon, Y Moriah, B Wajnryb), Contemp. Math. 164, Amer. Math. Soc. (1994) 231 MR1282766
21 M Stocking, Almost normal surfaces in $3$–manifolds, Trans. Amer. Math. Soc. 352 (2000) 171 MR1491877
22 A Thompson, Thin position and the recognition problem for $S^3$, Math. Res. Lett. 1 (1994) 613 MR1295555
23 F Waldhausen, On irreducible $3$–manifolds which are sufficiently large, Ann. of Math. $(2)$ 87 (1968) 56 MR0224099