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On families of fibred knots with equal Seifert forms
Communications in Analysis and Geometry ( IF 0.7 ) Pub Date : 2021-03-01 , DOI: 10.4310/cag.2021.v29.n2.a6
Filip Misev 1
Affiliation  

For every genus $g \geqslant 2$, we construct an infinite family of strongly quasipositive fibred knots $K_n$ having the same Seifert form as the torus knot $T(2, 2g + 1)$. In particular, their homological monodromies agree and their signatures and four-genera are maximal: $\lvert \sigma (K_n) \rvert = 2g_4 (K_n) = 2g$. On the other hand, the geometric stretching factors are pairwise distinct and the knots are pairwise not ribbon concordant.

中文翻译:

关于具有相同塞弗特形式的纤维结族

对于每个属$ g \ geqslant 2 $,我们构建一个无限准族的强拟正纤维结$ K_n $,其塞弗特形式与环结$ T(2,2g + 1)$相同。特别地,它们的同源性一元性一致,并且它们的签名和四属最大:$ \ lvert \ sigma(K_n)\ rvert = 2g_4(K_n)= 2g $。另一方面,几何拉伸因子是成对的,结是成对的而不是色带一致的。
更新日期:2021-04-20
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