Seifert-fibered surgeries which do not arise from primitive/Seifert-fibered constructions
نویسندگان
چکیده
منابع مشابه
On mapping cones of Seifert fibered surgeries
Using the mapping cone of a rational surgery, we give several obstructions for Seifert fibered surgeries, including obstructions on the Alexander polynomial, the knot Floer homology, the surgery coefficient and the Seifert and four-ball genus of the knot. These generalize the corresponding results in [9][21].
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We explore certain restrictions on knots in the three-sphere which admit non-trivial Seifert fibered surgeries. These restrictions stem from the Heegaard Floer homology (defined in [8]) for Seifert fibered spaces (compare [11]), and hence they have consequences for both the Alexander polynomial of such knots, and also their “knot Floer homology” (introduced in [10]). In particular, it is shown ...
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To each connected component in the space of semisimple representations from the orbifold fundamental group of the base orbifold of a Seifert fibered homology 3-sphere into the Lie group U(2, 1), we associate a real number called the “orbifold Toledo invariant.” Using the theory of Higgs bundles, we explicitly compute all values this invariant takes on.
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We show that if an orientable Seifert fibered space M with an orientable genus g base space admits a strongly irreducible horizontal Heegaard splitting then there is a one-to-one correspondence between isotopy classes of strongly irreducible horizontal Heegaard splittings and elements of Z. The correspondence is determined by the slopes of intersection of each Heegaard splitting with a collecti...
متن کاملSeifert fibered surgery on Montesinos knots
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: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03798-0