Volume 13, issue 4 (2009)

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Stabilization of Heegaard splittings

Joel Hass, Abigail Thompson and William Thurston

Geometry & Topology 13 (2009) 2029–2050
Bibliography
1 D Bachman, D Cooper, M E White, Large embedded balls and Heegaard genus in negative curvature, Algebr. Geom. Topol. 4 (2004) 31 MR2031911
2 I Chavel, Isoperimetric inequalities. Differential geometric and analytic perspectives, Cambridge Tracts in Math. 145, Cambridge Univ. Press (2001) MR1849187
3 J Eells, L Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978) 1 MR495450
4 J Eells, L Lemaire, Deformations of metrics and associated harmonic maps, Proc. Indian Acad. Sci. Math. Sci. 90 (1981) 33 MR653945
5 J Eells, J H Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964) 109 MR0164306
6 H Federer, Geometric measure theory, Grund. der math. Wissenschaften 153, Springer (1969) MR0257325
7 P Hartman, On homotopic harmonic maps, Canad. J. Math. 19 (1967) 673 MR0214004
8 J Hass, P Scott, The existence of least area surfaces in $3$–manifolds, Trans. Amer. Math. Soc. 310 (1988) 87 MR965747
9 R Kirby, Problems in low dimensional manifold theory, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., 1976), Part 2" (editor R J Milgram), Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc. (1978) 273 MR520548
10 Y N Minsky, Harmonic maps into hyperbolic $3$–manifolds, Trans. Amer. Math. Soc. 332 (1992) 607 MR1100698
11 E E Moise, Geometric topology in dimensions $2$ and $3$, Graduate Texts in Math. 47, Springer (1977) MR0488059
12 H Namazi, J Souto, Heegaard splittings and pseudo-Anosov maps, preprint
13 J T Pitts, J H Rubinstein, Applications of minimax to minimal surfaces and the topology of $3$–manifolds, from: "Miniconference on geometry and partial differential equations, 2 (Canberra, 1986)" (editors J E Hutchinson, L M Simon), Proc. Centre Math. Anal. Austral. Nat. Univ. 12, Austral. Nat. Univ. (1987) 137 MR924434
14 A W Reid, A non-Haken hyperbolic $3$–manifold covered by a surface bundle, Pacific J. Math. 167 (1995) 163 MR1318168
15 H Rubinstein, M Scharlemann, Comparing Heegaard splittings of non-Haken $3$–manifolds, Topology 35 (1996) 1005 MR1404921
16 J H Rubinstein, Minimal surfaces in geometric $3$–manifolds, from: "Global theory of minimal surfaces" (editor D Hoffman), Clay Math. Proc. 2, Amer. Math. Soc. (2005) 725 MR2167286
17 J H Sampson, Some properties and applications of harmonic mappings, Ann. Sci. École Norm. Sup. $(4)$ 11 (1978) 211 MR510549
18 M Scharlemann, Heegaard splittings of compact $3$–manifolds, from: "Handbook of geometric topology" (editors R J Daverman, R B Sher), North-Holland (2002) 921 MR1886684
19 J Schultens, The stabilization problem for Heegaard splittings of Seifert fibered spaces, Topology Appl. 73 (1996) 133 MR1416756
20 E Sedgwick, An infinite collection of Heegaard splittings that are equivalent after one stabilization, Math. Ann. 308 (1997) 65 MR1446199
21 J Singer, Three-dimensional manifolds and their Heegaard diagrams, Trans. Amer. Math. Soc. 35 (1933) 88 MR1501673