Dehn twists on nonorientable surfaces

• Autorzy: Michał Stukow
• Języki publikacji: EN

Abstrakty

EN

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, $I(tⁿ_{a}(b),b) = |n|I(a,b)²$, 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 by the twists is equal to the centre of ℳ(N) and is generated by twists about circles isotopic to boundary components of N.

Kategorie tematyczne

• 57N05: Topology of E 2 , 2 -manifolds
• 57M99: None of the above, but in this section
• 20F38: Other groups related to topology or analysis

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 2
• Strony: 117-147

Daty

wydano

2006

Twórcy

autor

Michał Stukow

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/fm189-2-3