Hostname: page-component-84b7d79bbc-g5fl4 Total loading time: 0 Render date: 2024-07-28T17:35:55.717Z Has data issue: false hasContentIssue false
  • English
  • Français

Full laminations in 3-manifolds

Published online by Cambridge University Press:  24 October 2008

A. Hatcher  and
U. Oertel
A. Hatcher
Affiliation:
Cornell University, Ithaca NY 14853-7901, U.S.A
U. Oertel
Affiliation:
Rutgers University, Newark NJ 07102, U.S.A
Get access Rights & Permissions [Opens in a new window]

Extract

Essential laminations in 3-manifolds, introduced in [GO], are a natural generalization of both incompressible surfaces and foliations without Reeb components. One of the main reasons why essential laminations are of particular interest is that many manifolds which contain no incompressible surfaces contain essential laminations. Indeed, there is some evidence that almost all irreducible manifolds with infinite fundamental group contain essential laminations [B1; D; GM; GO; H; N; R], the only known exceptions being Seifert manifolds [B2]. So essential laminations are potentially a quite powerful tool for studying non-Haken 3-manifolds.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 1 , January 1996 , pp. 73 - 82
Copyright
Copyright © Cambridge Philosophical Society 1996

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

[B1]Brittenham, M.. An essential lamination in the Seifert-Weber space, preprint.Google Scholar
[B2]Brittenham, M.. Essential laminations in Seifert fiber spaces, preprint.Google Scholar
[CGLS]Culler, M., Gordon, C., Luecke, J. and Shalen, P.. Dehn surgery on knots. Annals of Math. 125 (1987), 237–300.CrossRefGoogle Scholar
[D]Delman, C.. Dehn surgery on 2-bridge knots. Top. and its Appl, to appear.Google Scholar
[FLP]Fathi, A., Laudenbach, F. and Poénaru, V.. Travaux de Thurston sur les surfaces. Astérisque 66–67 (1979).Google Scholar
[GM]Gabai, D. and Mosher, L.. (in preparation).Google Scholar
[GO]Gabai, D. and Oertel, U.. Essential laminations in 3-manifolds. Annals of Math. 130 (1989), 41–73.CrossRefGoogle Scholar
[H]Hatcher, A.. Some examples of essential laminations in 3-manifolds. Ann. Inst. Fourier 42 (1992), 313–325.CrossRefGoogle Scholar
[N]Naimi, R.. Constructing essential laminations in some 3-manifolds, thesis (Caltech, 1992).Google Scholar
[R]Roberts, R.. Constructing taut foliations, thesis (Cornell, 1992).Google Scholar
[M]Menasco, W.. Closed incompressible surfaces in alternating knot and link complements. Topology 23 (1984), 37–44.CrossRefGoogle Scholar
[W1]Ying-Qing, Wu.Incompressibility of surfaces in surgered 3-manifolds. Topology 31 (1992), 271–279.Google Scholar
[W2]Ying-Qing, Wu.Essential laminations in surgered 3-manifolds. Proc. A.M.S. 115 (1992), 245–249.Google Scholar