Computations of the Ozsvath-Szabo knot concordance invariant
Computations of the Ozsvath-Szabo knot concordance invariant
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DOI：
10.2140/gt.2004.8.735
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发表时间：
2004-01-01
影响因子：
2
通讯作者：
Livingston, C
中科院分区：
文献类型：
--
作者：
Livingston, C
Ozsvath和Szabo定义了一个纽结和谐不变量τ，它限定了纽结的4球亏格。在这里，我们讨论它的计算捷径。我们包括亚历山大多项式的例子，一个不变量是非平凡的结，包括所有迭代解扭的正双结与非负Thurston-Bennequin数，如三叶草，并明确计算几个10交叉结。我们还注意到，一个新的证明切片-Bennequin不等式很快从这些技术。
Ozsvath and Szabo have defined a knot concordance invariant tau that bounds the 4-ball genus of a knot. Here we discuss shortcuts to its computation. We include examples of Alexander polynomial one knots for which the invariant is nontrivial, including all iterated untwisted positive doubles of knots with nonnegative Thurston-Bennequin number, such as the trefoil, and explicit computations for several 10 crossing knots. We also note that a new proof of the Slice-Bennequin Inequality quickly follows from these techniques.