Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T12:29:32.440Z Has data issue: false hasContentIssue false
  • English
  • Français

Berge's distance 3 pairs of genus 2 Heegaard splittings

Published online by Cambridge University Press:  27 April 2011

MARTIN SCHARLEMANN
MARTIN SCHARLEMANN*
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106U.S.A e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Following an example discovered by John Berge [2], we show that there is a 4-component link L ⊂ (S1 × S2)#(S1 × S2) so that, generically, the result of Dehn surgery on L is a 3-manifold with two inequivalent genus 2 Heegaard splittings, and each of these Heegaard splittings is of Hempel distance 3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 151 , Issue 2 , September 2011 , pp. 293 - 306
Copyright
Copyright © Cambridge Philosophical Society 2011

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]Berge, J. A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody, arXiv:0910.3038.Google Scholar
[2]Berge, J. A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings, arXiv:0912.1315.Google Scholar
[3]Berge, J. and Scharlemann, M. Multiple genus 2 Heegaard splittings: a missed case, arXiv:0910.3921.Google Scholar
[4]Hempel, J.3-manifolds as viewed from the curve complex. Topology 40 (2001), 631–657.CrossRefGoogle Scholar
[5]Rubinstein, H. and Scharlemann, M.Genus two Heegaard splittings of orientable 3-manifolds, in Proceedings of the 1998 Kirbyfest. Geometry and Topology Monographs 2 (1999), 489–553.CrossRefGoogle Scholar
[6]Thompson, A.The disjoint curve property and genus 2 manifolds. Topology Appl. 97 (1999), 273–279.CrossRefGoogle Scholar