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Dehn twists on nonorientable surfaces

Dehn twists on nonorientable surfaces

Let $t_a$ be the Dehn twist about a circle $a$ on an orientable surface. It is well known that for each circle $b$ and an integer $n$, $I(t_a^n(b),b)=|n|I(a,b)^2$, where $I(\cdot,\cdot)$ is the geometric intersection number. We prove a similar formula for