Mathematische Annalen

, Volume 280, Issue 2, pp 191–205 | Cite as

Unknotting number, genus, and companion tori

  • Martin Scharlemann
  • Abigail Thompson
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B]
    Bleiler, S.: Prime tangles and composite knots. In: Knot theory and manifolds. Lecture Notes 1144, pp. 1–13. Berlin, Heidelberg, New York: Springer 1985Google Scholar
  2. [E]
    Eudave-Muñoz, M.: Cirugia en nudos fuertemente invertibles. An. Inst. Mat. U.N.A.M. 26, 41–57 (1986)Google Scholar
  3. [Ga1]
    Gabai, D.: Foliations and the topology of 3-manifolds, II. J. Differ. Geom.26, 461–478 (1987)Google Scholar
  4. [Ga2]
    Gabai, D.: Genus is superadditive under band-connected sum. Topology26, 209–210 (1987)Google Scholar
  5. [GL]
    Gordon, C., Luecke, J.: Only integral Dehn surgeries can yield reducible manifolds. Math. Proc. Cam. Phil. Soc.102, 97–101 (1987)Google Scholar
  6. [L]
    Lyon, H.: Simple knots without unique minimal surfaces. Proc. Am. Math. Soc.43, 449–454 (1974)Google Scholar
  7. [M]
    Myers, R.: Simple knots in compact, orientable 3-manifolds. Trans. Am. Math. Soc.273, 75–91 (1982)Google Scholar
  8. [S1]
    Scharlemann, M.: Smooth spheres in ℝ4 with four critical points are standard. Invent. Math.79, 125–141 (1985)Google Scholar
  9. [S2]
    Scharlemann, M.: Unknotting number one knots are prime. Invent. Math.82, 37–55 (1985)Google Scholar
  10. [S3]
    Scharlemann, M.: Sutured manifolds and generalized Thurston norms. To appear in J. Differ. Geom.Google Scholar
  11. [T]
    Thompson, A.: PropertyP for the band-connect sum of two knots. Topology26, 205–208 (1987)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Martin Scharlemann
    • 1
  • Abigail Thompson
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Personalised recommendations