The slope conjecture relates the degree of the colored Jones polynomial of a knot to boundary slopes of essential surfaces. We develop a general approach that matches a state-sum formula for the colored Jones polynomial with the parameters that describe surfaces in the complement. We apply this to Montesinos knots proving the slope conjecture for Montesinos knots, with some restrictions.

中文翻译：

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Montesinos 结的斜率猜想

斜率猜想将结的彩色琼斯多项式的次数与基本表面的边界斜率联系起来。我们开发了一种通用方法，该方法将彩色琼斯多项式的状态和公式与在补码中描述表面的参数相匹配。我们将此应用于蒙特西诺斯结，证明蒙特西诺斯结的斜率猜想，但有一些限制。