Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T06:58:23.807Z Has data issue: false hasContentIssue false
  • English
  • Français

Small 3-manifolds with large Heegaard distance

Published online by Cambridge University Press:  22 July 2013

TAO LI
TAO LI*
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467U.S.A. e-mail: taoli@bc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We construct examples of closed non-Haken hyperbolic 3-manifolds with a Heegaard splitting of arbitrarily large distance.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 3 , November 2013 , pp. 431 - 441
Copyright
Copyright © Cambridge Philosophical Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Agol, IanSmall 3-manifolds of large genus. Geom. Dedicata 102 (2003), 53–64.CrossRefGoogle Scholar
[2]Finkelstein, E. and Moriah, Y.Closed incompressible surfaces in knot complements. Trans. Amer. Math. Soc. 352 (2000), 655–677.CrossRefGoogle Scholar
[3]Floyd, W. and Hatcher, A.Incompressible surfaces in punctured-torus bundles. Topology Appl. 13 (1982), 263–282.CrossRefGoogle Scholar
[4]Hartshorn, K.Heegaard splittings of Haken manifolds have bounded distance. Pacific J. Math. 204 (2002), 61–75.CrossRefGoogle Scholar
[5]Harvey, W. J.Boundary structure of the modular group. Ann. of Math. Stud. 97 (Princeton, 1981), 245–251.Google Scholar
[6]Hatcher, A.On the boundary curves of incompressible surfaces. Pacific J. Math. 99 (1982), 373–377.CrossRefGoogle Scholar
[7]Hatcher, A. and Thurston, W.Incompressible surfaces in 2-bridge knot complements. Invent. Math. 79 (1985), 225–249.CrossRefGoogle Scholar
[8]Hempel, J.3–manifolds as viewed from the curve complex. Topology 40 (2001), 631–657.CrossRefGoogle Scholar
[9]Li, T.Heegaard surfaces and measured laminations, I: the Waldhausen conjecture. Invent. Math. 167 (2007), 135–177.CrossRefGoogle Scholar
[10]Li, T.Heegaard surfaces and measured laminations, II: non-Haken 3–manifolds. J. Amer. Math. Soc. 19 (2006), 625–657.CrossRefGoogle Scholar
[11]Li, T.Saddle tangencies and the distance of Heegaard splittings. Algebr. Geom. Topol. 7 (2007), 1119–1134.CrossRefGoogle Scholar
[12]Li, T.Heegaard surfaces and the distance of amalgamation. Geome. Topol. 14 (2010), 1871–1919.CrossRefGoogle Scholar
[13]Lustig, M. and Moriah, Y.Closed incompressible surfaces in complements of wide knots and links. Topology Appl. 92 (1999), 1–13.CrossRefGoogle Scholar
[14]Lustig, M. and Moriah, Y.High distance Heegaard splittings via fat train tracks. Topology Appl. 156 (2009), 1118–1129.CrossRefGoogle Scholar
[15]Masur, H. and Minsky, Y.Geometry of the complex of curves I: Hyperbolicity. Invent. Math. 138 (1999), 103–149.CrossRefGoogle Scholar
[16]Oertel, U.Closed incompressible surfaces in complements of star links. Pacific J. Math. 111 (1984), 209–230.CrossRefGoogle Scholar
[17]Scharlemann, M. and Tomova, M.Alternate Heegaard genus bounds distance. Geome. Topol. 10 (2006), 593–617.CrossRefGoogle Scholar
[18]Waldhausen, F.On irreducible 3-manifolds which are sufficiently large. Ann. of Math. (2) 87 (1968), 56–88.CrossRefGoogle Scholar