Basic question on Dehn twists - Mathematics Stack Exchange
2023年11月26日 · Order of the images of Dehn twists in the quantum representation of Reshetikhin-Turaev TQFT and relation to Vafa's theorem Hot Network Questions How does VIM know to NOT interpret this .html file as html?
geometric topology - Dehn Twist Actions on Surface Homology ...
2024年10月15日 · But also there is no natural way at all to pick a Dehn twist assigned to an arbitrary homology class (outside of just picking a random, meaningless assignment): the identity homology class has too many simple closed curves representing it; some homology classes have no simple closed representatives at all.
riemannian geometry - Dehn twist as isometries on hyperbolic …
2015年1月30日 · A Dehn twist is not an isometry of the hyperbolic surface: to convince you about this, consider any curve $\eta$ transversally intersecting $\gamma$. As you perform the Dehn twist around $\gamma$, $\eta$ has to travel along $\gamma$ for a complete turn, before crossing it. Therefore its length increases proportionally to the length of $\gamma$.
Understanding Monodromy by examples - Mathematics Stack …
2014年2月20日 · The Dehn twist operation will be to take the red curve and replace a neighborhood of it near the green curve with a curve that goes once around the cylinder. The singular fiber is meant to be blue. If we consider the two curves parallel and unlinked on the left, then on the right the linking number of the red and blue curves is 1, i.e the red ...
homotopy theory - Dehn twists are non-trivial infinite order …
Dehn twist is not $\displaystyle{1_{G}}$ in $\displaystyle{MAP(S)}$ and is infinite order. So, we want to show that: Dehn twists are non-trivial infinite order elements in $\displaystyle{MAP(S)}$ . I want help to proof the above.
The monodromy of a Lefschetz fibration as right-handed Dehn twists
2019年11月26日 · He shows the monodromy is a generalized Dehn twist about S^n-1. For four manifolds the local model will be T^*S^1 and it will be a usual Dehn twist. This generalized Dehn twist observation is originally due to Arnold so he probably has a paper about it as well in the 80s or 90s which might be an nicer read.
Dehn twist and length of a curve. - Mathematics Stack Exchange
A stronger statement (I guess!) ("Dehn twist fixed all geodesics not intersecting the simple closed curve.") was mentioned Here without any proof. It seems true from definition but I don't know how to prove it.
Why does Dehn twist about the inner circle of of an annulus
The Dehn twist does take the curve on the left to the curve on the right, the curves are just (properly) isotopic! The reason is that you are allowed to slide the endpoints as long as they stay on the boundary.
Dehn twist generators for mapping class group of a punctured disc
2018年1月10日 · But I cannot find explicit Dehn twist generators based on that question at the moment (apparently Dehn twists about the curves $\alpha$ and $\beta$ there are two of the generators, but I do not know how that answer counts boundary Dehn twists as part of …
Half-twist (Dehn twist) on braids represented as elements of the ...
2022年6月10日 · Half-twist (Dehn twist) on braids represented as elements of the mapping class group on an n-punctures disk.