Geodesic
Heegaard splittings of distance exactly n
Ido, Ayako1 ; Jang, Yeonhee1 ; Kobayashi, Tsuyoshi1
1Department of Mathematics, Nara Women’s University, Kitauoya Nishimachi, Nara 630-8506, Japan
Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1395-1411
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In this paper, we show that, for any integers n ≥ 2 and g ≥ 2, there exist genus-g Heegaard splittings of compact 3–manifolds with distance exactly n.

DOI : 10.2140/agt.2014.14.1395
Classification : 57M27, 57M99
Keywords: Heegaard splittings, Hempel distance, distance, Heegaard splitting

Ido, Ayako  1   ; Jang, Yeonhee  1   ; Kobayashi, Tsuyoshi  1

1 Department of Mathematics, Nara Women’s University, Kitauoya Nishimachi, Nara 630-8506, Japan 
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Ido, Ayako; Jang, Yeonhee; Kobayashi, Tsuyoshi. Heegaard splittings of distance exactly n. Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1395-1411. doi: 10.2140/agt.2014.14.1395

[1] A Abrams, S Schleimer, Distances of Heegaard splittings, Geom. Topol. 9 (2005) 95

[2] J Berge, M Scharlemann, Multiple genus $2$ Heegaard splittings: A missed case, Algebr. Geom. Topol. 11 (2011) 1781

[3] T Evans, High distance Heegaard splittings of $3$–manifolds, Topology Appl. 153 (2006) 2631

[4] Q Guo, R Qiu, Y Zou, The Heegaard distances cover all non-negative integers,

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

[6] W J Harvey, Boundary structure of the modular group, from: "Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference" (editors I Kra, B Maskit), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 245

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

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

[9] T Kobayashi, Y Rieck, Manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings, Comm. Anal. Geom. 17 (2009) 637

[10] T Li, Images of the disk complex, Geom. Dedicata 158 (2012) 121

[11] J Ma, R Qiu, Y Zou, Heegaard distances cover all non-negative integers, preprint

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

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

[14] S Schleimer, Notes on the complex of curves (2006)

[15] A Thompson, The disjoint curve property and genus $2$–manifolds, Topology Appl. 97 (1999) 273

[16] M Yoshizawa, High distance Heegaard splittings via Dehn twists, to appear in Algebr. Geom. Topol. (2014)

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