Chromatic Homotopy Theory
《Chromatic Homotopy Theory》 · 第 187 页 · Section 6.5.3，Dehn twists（函数区间与公式核对原页）
Let \(\gamma\) be a non-trivial simple closed curve in the interior of \(S_{g,b,p}\). The Dehn twist along \(\gamma\) is the element \(T_\gamma\in\operatorname{MCG}(S_{g,b,p})\) defined as follows. Pick a tubular neighbourhood of \(\gamma\) orientation-preservingly diffeomorphic to \(S^1\times[-1,1]\) where \(\gamma\) lies as \(S^1\times\{0\}\). Let \(f:[-1,1]\to\mathbb R\) be a smooth function which is zero in \([-1,-\frac12]\) and \(2\pi\) on \([\frac12,1]\). Let \(T_\gamma:S_{g,b,p}\longrightarrow S_{g,b,p}\) be the diffeomorphism that acts on the tubular neighbourhood as \(T_\gamma(e^{i\alpha},t)=(e^{i(\alpha+f(t))},t)\) and on its complementary set in \(S_{g,b,p}\) as the identity.