Incompressible surfaces in 2-bridge knot complements

1985 ◽  
Vol 79 (2) ◽  
pp. 225-246 ◽  
Author(s):  
A. Hatcher ◽  
W. Thurston
Keyword(s):  
Incompressible Surfaces ◽  
Knot Complements

scholarly journals Closed incompressible surfaces in knot complements

1999 ◽  
Vol 352 (2) ◽  
pp. 655-677 ◽  
Author(s):  
Elizabeth Finkelstein ◽  
Yoav Moriah
Keyword(s):  
Incompressible Surfaces ◽  
Knot Complements

Accidental surfaces in knot complements

2000 ◽  
Vol 09 (06) ◽  
pp. 725-733 ◽  
Author(s):  
Kazuhiro Ichihara ◽  
Makoto Ozawa
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Incompressible Surface ◽  
Incompressible Surfaces ◽  
Parallel Surface ◽  
Seifert Surfaces ◽  
Knot Complements ◽  
Necessary And Sufficient

It is well known that for many knot classes in the 3-sphere, every closed incompressible surface in their complements contains an essential loop which is isotopic into the boundary of the knot exterior. In this paper, we investigate closed incompressible surfaces in knot complements with this property. We show that if a closed, incompressible, non-boundary-parallel surface in a knot complement has such loops, then they determine the unique slope on the boundary of the knot exterior. Moreover, if the slope is non-meridional, then such loops are mutually isotopic in the surface. As an application, a necessary and sufficient condition for knots to bound totally knotted Seifert surfaces is given.

scholarly journals Least area incompressible surfaces in 3-manifolds

1983 ◽  
Vol 71 (3) ◽  
pp. 609-642 ◽  
Author(s):  
Michael Freedman ◽  
Joel Hass ◽  
Peter Scott
Keyword(s):  
Incompressible Surfaces ◽  
Least Area
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