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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 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...

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