Least area Seifert surfaces and periodic knots
نویسندگان
چکیده
منابع مشابه
Knots with Infinitely Many Incompressible Seifert Surfaces
We show that a knot in S with an infinite number of incompressible Seifert surfaces contains a closed incompressible surface in its complement.
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We will use immersed surfaces to study Seifert fibered surgery on Montesinos knots, and show that if 1 q1−1 + 1 q2−1 + 1 q3−1 ≤ 1 then a Montesinos knot K(p q1 , p2 q2 , p3 q3 ) admits no atoroidal Seifert fibered surgery.
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Here, a surface is smooth, compact, oriented, and has no component with empty boundary. A Seifert surface is a surface embedded in S3. A subsurface S of a surface T is full if each simple closed curve on S that bounds a disk on T already bounds a disk on S. The definition of quasipositivity is recalled in §1, after a review of braided surfaces. The “only if” statement of the Characterization Th...
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Exceptional Dehn surgeries on arborescent knots have been classified except for Seifert fibered surgeries on Montesinos knots of length 3. There are infinitely many of them as it is known that 4n + 6 and 4n + 7 surgeries on a (−2, 3, 2n + 1) pretzel knot are Seifert fibered. It will be shown that there are only finitely many others. A list of 20 surgeries will be given and proved to be Seifert ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1984
ISSN: 0166-8641
DOI: 10.1016/0166-8641(84)90003-8