Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Incompressible surfaces in link complements


Author: Ying-Qing Wu
Journal: Proc. Amer. Math. Soc. 129 (2001), 3417-3423
MSC (1991): Primary 57N10, 57M25
DOI: https://doi.org/10.1090/S0002-9939-01-05938-X
Published electronically: April 2, 2001
MathSciNet review: 1845021
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

We generalize a theorem of Finkelstein and Moriah and show that if a link $L$ has a $2n$-plat projection satisfying certain conditions, then its complement contains some closed essential surfaces. In most cases these surfaces remain essential after any totally nontrivial surgery on $L$.


References [Enhancements On Off] (What's this?)

  • [BZ] G. Burde and H. Zieschang, Knots, de Gruyter Studies in Math. 5, 1985. MR 87b:57004
  • [CGLS] M. Culler, C. Gordon, J. Luecke and P. Shalen, Dehn surgery on knots, Annals Math. 125 (1987), 237-300. MR 88a:57026; correction MR 89c:57015
  • [FM1] E. Finkelstein and Y. Moriah, Closed incompressible surfaces in knot complements, Trans. Amer. Math. Soc. 352 (2000), 655-677. MR 2000c:57007
  • [FM2] -, Tubed incompressible surfaces in knot and link complements, Topology Appl. 96 (1999), 153-170. CMP 99:16
  • [HT] A. Hatcher and W. Thurston, Incompressible surfaces in 2-bridge knot complements, Inv. Math. 79 (1985), 225-246. MR 86g:57003
  • [Me] W. Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984), 37-44. MR 86b:57004
  • [Sch] M. Scharlemann, Producing reducible 3-manifolds by surgery on a knot, Topology 29 (1990), 481-500. MR 91i:57003
  • [Wu] Y-Q. Wu, The classification of nonsimple algebraic tangles, Math. Ann. 304 (1996), 457-480. MR 97b:57010

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57N10, 57M25

Retrieve articles in all journals with MSC (1991): 57N10, 57M25


Additional Information

Ying-Qing Wu
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: wu@math.uiowa.edu

DOI: https://doi.org/10.1090/S0002-9939-01-05938-X
Keywords: Incompressible surfaces, $2n$-plat projections, Dehn surgery
Received by editor(s): February 22, 2000
Received by editor(s) in revised form: March 27, 2000
Published electronically: April 2, 2001
Additional Notes: The author was supported in part by NSF grant #DMS 9802558.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society