Dehn twists on nonorientable surfaces

Michał Stukow. "Dehn twists on nonorientable surfaces." Fundamenta Mathematicae 189.2 (2006): 117-147. <http://eudml.org/doc/286552>.

@article{MichałStukow2006,
abstract = {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.},
author = {Michał Stukow},
journal = {Fundamenta Mathematicae},
keywords = {mapping class groups; nonorientable surfaces; Dehn twists; boundary components; punctures; centralizer; center},
language = {eng},
number = {2},
pages = {117-147},
title = {Dehn twists on nonorientable surfaces},
url = {http://eudml.org/doc/286552},
volume = {189},
year = {2006},
}

TY - JOUR
AU - Michał Stukow
TI - Dehn twists on nonorientable surfaces
JO - Fundamenta Mathematicae
PY - 2006
VL - 189
IS - 2
SP - 117
EP - 147
AB - 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.
LA - eng
KW - mapping class groups; nonorientable surfaces; Dehn twists; boundary components; punctures; centralizer; center
UR - http://eudml.org/doc/286552
ER -