Geodesic
Heegaard splittings with large subsurface distances
Johnson, Jesse1 ; Minsky, Yair2 ; Moriah, Yoav3
1Department of Mathematics, Oklahoma State University, 401 MSCS, Stillwater OK 74078, USA
2Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven CT 06520-8283, USA
3Department of Mathematics, Technion, 32000 Haifa, Israel
Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2251-2275
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We show that subsurfaces of a Heegaard surface for which the relative Hempel distance of the splitting is sufficiently high have to appear in any Heegaard surface of genus bounded by half that distance.

DOI : 10.2140/agt.2010.10.2251
Keywords: Heegaard splitting, curve complex, subsurface projection

Johnson, Jesse  1   ; Minsky, Yair  2   ; Moriah, Yoav  3

1 Department of Mathematics, Oklahoma State University, 401 MSCS, Stillwater OK 74078, USA
2 Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven CT 06520-8283, USA
3 Department of Mathematics, Technion, 32000 Haifa, Israel 
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Johnson, Jesse; Minsky, Yair; Moriah, Yoav. Heegaard splittings with large subsurface distances. Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2251-2275. doi: 10.2140/agt.2010.10.2251

[1] D Bachman, S Schleimer, Surface bundles versus Heegaard splittings, Comm. Anal. Geom. 13 (2005) 903

[2] D Bachman, S Schleimer, E Sedgwick, Sweepouts of amalgamated $3$–manifolds, Algebr. Geom. Topol. 6 (2006) 171

[3] J F Brock, R D Canary, Y N Minsky, The classification of Kleinian surface groups II: the ending lamination conjecture, to appear in Ann. of Math. $(2)$

[4] B Farb, A Lubotzky, Y Minsky, Rank–$1$ phenomena for mapping class groups, Duke Math. J. 106 (2001) 581

[5] K Hartshorn, Heegaard splittings of Haken manifolds have bounded distance, Pacific J. Math. 204 (2002) 61

[6] J Hempel, $3$–Manifolds, Ann. of Math. Studies 86, Princeton Univ. Press (1976)

[7] J Hempel, $3$–manifolds as viewed from the curve complex, Topology 40 (2001) 631

[8] N V Ivanov, The rank of Teichmüller modular groups, Mat. Zametki 44 (1988) 636, 701

[9] N V Ivanov, Subgroups of Teichmüller modular groups, Transl. of Math. Monogr. 115, Amer. Math. Soc. (1992)

[10] J Johnson, Surface bundles with genus two Heegaard splittings, J. Topol. 1 (2008) 671

[11] J Johnson, Stable functions and common stabilizations of Heegaard splittings, Trans. Amer. Math. Soc. 361 (2009) 3747

[12] T Kobayashi, Heights of simple loops and pseudo-Anosov homeomorphisms, from: "Braids (Santa Cruz, CA, 1986)" (editors J S Birman, A Libgober), Contemp. Math. 78, Amer. Math. Soc. (1988) 327

[13] T Kobayashi, O Saeki, The Rubinstein–Scharlemann graphic of a $3$–manifold as the discriminant set of a stable map, Pacific J. Math. 195 (2000) 101

[14] M Lackenby, The Heegaard genus of amalgamated $3$–manifolds, Geom. Dedicata 109 (2004) 139

[15] H A Masur, Y N Minsky, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math. 138 (1999) 103

[16] H A Masur, Y N Minsky, Geometry of the complex of curves. II. Hierarchical structure, Geom. Funct. Anal. 10 (2000) 902

[17] J N Mather, Stability of $C^{\infty }$ mappings. V. Transversality, Advances in Math. 4 (1970)

[18] Y Minsky, The classification of Kleinian surface groups. I. Models and bounds, Ann. of Math. $(2)$ 171 (2010) 1

[19] H Rubinstein, M Scharlemann, Comparing Heegaard splittings of non-Haken $3$–manifolds, Topology 35 (1996) 1005

[20] M Scharlemann, M Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006) 593

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