Geometry & Topology Volume 15, issue 2 (2011)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

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

Tao Li

Geometry & Topology 15 (2011) 1029–1106

DOI: 10.2140/gt.2011.15.1029

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