Twist families of $L$-space knots, their genera, and Seifert surgeries
نویسندگان
چکیده
منابع مشابه
The Sl2(c) Casson Invariant for Seifert Fibered Homology Spheres and Surgeries on Twist Knots
We derive a simple closed formula for the SL2(C) Casson invariant for Seifert fibered homology 3-spheres using the correspondence between SL2(C) character varieties and moduli spaces of parabolic Higgs bundles of rank two. These results are then used to deduce the invariant for Dehn surgeries on twist knots by combining computations of the Culler-Shalen norms with the surgery formula for the SL...
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Using Hirasawa-Murasugi’s classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman-Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on S. We also construct L-space knots with arbitrarily larg...
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Let K be a non-trivial knot in the 3-sphere with a lens space surgery and L(p, q) a lens space obtained by a Dehn surgery on K. We study a relationship between the order |p| of the fundamental group of L(p, q) and the Seifert genus g of K. Considering certain infinite families of knots with lens space surgeries, the following estimation is suggested as a conjecture: 2g + 2 √ 40g + 1 5 + 3 5 ≤ |...
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It is proved that every knot in the major subfamilies of J. Berge’s lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped (real) plane curve as a divide knot defined by N. A’Campo in the context of singularity theory of complex curves. For each knot given by Berge’s parameters, the corresponding plane curve is constructed. The surgery coefficients ar...
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We define a filtration on the vector space spanned by Seifert matrices of knots related to Vassiliev’s filtration on the space of knots. Further we show that the invariants of knots derived from the filtration can be expressed by coefficients of the Alexander polynomial. The theory of finite type invariants (Vassiliev invariants) for knots was first introduced by V. Vassiliev [13] and reformula...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2019
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2019.v27.n4.a1