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Dehn twists on nonorientable surfaces

Michał Stukow — 2006

Fundamenta Mathematicae

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, $I (t ⁿ_{a} (b), b) = | n | I (a, b) ²$ , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup of ℳ(N) generated...

Involving symmetries of Riemann surfaces to a study of the mapping class group.

Grzegorz Gromadzki; Michal Stukow — 2004

Publicacions Matemàtiques

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