We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using $\nu^+$ from the Heegaard Floer knot complex and explicit constructions of cobordisms. As an application, we determine the pairs of torus knots related by a single crossing change. Also, we determine the pairs of Thurston-Bennequin number maximizing Legendrian torus knots that have a genus one exact Lagrangian cobordism, with one exception.

中文翻译：

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环面结之间的属一协同

我们确定了一对环面结，它们之间具有一个共边关系，但有一个明显的例外。这是通过使用来自 Heegaard Floer 结复合体的 $\nu^+$ 和 cobordisms 的显式构造组合障碍物来完成的。作为一个应用程序，我们确定与单个交叉变化相关的环面结对。此外，我们确定了 Thurston-Bennequin 数对最大化 Legendrian 圆环结，这些结具有一个精确的拉格朗日坐标系，但有一个例外。