Some examples of essential laminations in 3-manifolds

Allen Hatcher

Annales de l'institut Fourier (1992)

  • Volume: 42, Issue: 1-2, page 313-325
  • ISSN: 0373-0956

Abstract

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Families of codimension-one foliations and laminations are constructed in certain 3-manifolds, with the property that their transverse intersection with the boundary torus of the manifold consists of parallel curves whose slope varies continuously with certain parameters in the construction. The 3-manifolds are 2-bridge knot complements and punctured-torus bundles.

How to cite

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Hatcher, Allen. "Some examples of essential laminations in 3-manifolds." Annales de l'institut Fourier 42.1-2 (1992): 313-325. <http://eudml.org/doc/74955>.

@article{Hatcher1992,
abstract = {Families of codimension-one foliations and laminations are constructed in certain 3-manifolds, with the property that their transverse intersection with the boundary torus of the manifold consists of parallel curves whose slope varies continuously with certain parameters in the construction. The 3-manifolds are 2-bridge knot complements and punctured-torus bundles.},
author = {Hatcher, Allen},
journal = {Annales de l'institut Fourier},
keywords = {boundary slope; Families of codimension-one foliations; laminations; 3- manifold; 2-bridge knot complements; punctured-torus bundles},
language = {eng},
number = {1-2},
pages = {313-325},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some examples of essential laminations in 3-manifolds},
url = {http://eudml.org/doc/74955},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Hatcher, Allen
TI - Some examples of essential laminations in 3-manifolds
JO - Annales de l'institut Fourier
PY - 1992
PB - Association des Annales de l'Institut Fourier
VL - 42
IS - 1-2
SP - 313
EP - 325
AB - Families of codimension-one foliations and laminations are constructed in certain 3-manifolds, with the property that their transverse intersection with the boundary torus of the manifold consists of parallel curves whose slope varies continuously with certain parameters in the construction. The 3-manifolds are 2-bridge knot complements and punctured-torus bundles.
LA - eng
KW - boundary slope; Families of codimension-one foliations; laminations; 3- manifold; 2-bridge knot complements; punctured-torus bundles
UR - http://eudml.org/doc/74955
ER -

References

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  1. [B] M. BRITTENHAM, Essential laminations in Seifert-fibered spaces, preprint. Zbl0791.57013
  2. [FH1] W. FLOYD and A. HATCHER, The space of incompressible surfaces in a 2-bridge link complement, Trans. A.M.S., 305 (1988), 575-599. Zbl0672.57006MR89c:57004
  3. [FH2] W. FLOYD and A. HATCHER, Incompressible surfaces in punctured-torus bundles, Topology and its Appl., 13 (1982), 263-282. Zbl0493.57004MR83h:57015
  4. [G] D. GABAI, Laminations transverse to foliations, to appear. Zbl0888.57025
  5. [GO] D. GABAI and U. OERTEL, Essential laminations in 3-manifolds, Annals of Math., 130 (1989), 41-73. Zbl0685.57007MR90h:57012
  6. [H] A. HATCHER, On the boundary curves of incompressible surfaces, Pac. J. Math., 99 (1982), 373-377. Zbl0502.57005MR83h:57016
  7. [HO] A. HATCHER and U. OERTEL, Affine lamination spaces for surfaces, Pac. J. Math., to appear. Zbl0772.57032
  8. [HT] A. HATCHER and W. THURSTON, Incompressible surfaces in 2-bridge knot complements, Invent. Math., 79 (1985), 225-246. Zbl0602.57002MR86g:57003
  9. [JN] M. JANKINS and W. NEUMANN, Rotation numbers of products of circle homeomorphisms, Math. Annalen, 271 (1985), 381-400. Zbl0543.57019MR86g:58082

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