Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T04:43:45.752Z Has data issue: false hasContentIssue false
  • English
  • Français

Which 3-Manifolds Embed in Triod × I × I?

Published online by Cambridge University Press:  20 November 2018

Dale Rolfsen  and
Li Zhongmou
Dale Rolfsen
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, e-mail: [email protected]
Li Zhongmou
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We classify the compact 3-manifolds whose boundary is a union of 2-spheres, and which embed in T ×I ×I, where T is a triod and I the unit interval. This class is described explicitly as the set of punctured handlebodies. We also show that any 3-manifold in T × I × I embeds in a punctured handlebody.

Keywords

57N1057N3557Q35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 3 , 01 September 1997 , pp. 370 - 375
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Gillman, David, The Poincaré conjecture is true in the product of any graph with a disc, Proc. Amer. Math. Soc. 110 (1990), 829–834.Google Scholar
2. Gillman, David and Rolfsen, Dale, Three-manifolds embed in small 3-complexes, Internat. J. Math. 3 (1992), 179–183.Google Scholar
3. Hempel, John, 3-manifolds, Princeton Univ. Press, 1976.Google Scholar
4. Zhongmou, Li, Every 3-manifold with boundary embeds in Triod × Triod × I, Proc. Amer. Math. Soc. 112 (1994), 575–579.Google Scholar