All Questions
7 questions
4
votes
0
answers
116
views
Do any Legendrian knots in standard contact 3-space have big tubular neighborhoods?
Consider $\mathbb{R}^3$ with the standard contact structure $\ker(dz-y\,dx)$.
According to the contact version of Weinstein's theorem, any Legendrian knot $L\subset \mathbb{R}^3$ has a tubular ...
- 491
3
votes
0
answers
87
views
Are these contact structures on the open solid torus diffeomorphic?
Let $M=S^1\times \mathbb{R}^2$ and $\alpha_1, \alpha_2$ be a pair of contact one-forms on $M$ such that the restrictions $\alpha_1|_{S^1\times \{0\}}$, $\alpha_2|_{S^1\times \{0\}}$ coincide and ...
- 491
3
votes
2
answers
199
views
Effect of a Lutz twist on Euler number
I already asked this question on the Math Stack Exchange but did not get an answer.
I am currently working through Geiges proof of the Martinet-Lutz theorem, which can be
found here, and am trying to ...
1
vote
0
answers
60
views
Global solutions for an analytic family of differential operators with initial condition
This is related to this other question question of mine.
Let $M$ be a $3$-dimensional closed (compact without boundary) strongly pseudoconvex manifold and let $\Delta_t$ be a collection of ...
- 1,409
15
votes
3
answers
2k
views
Examples of odd-dimensional manifolds that do not admit contact structure
I'm having an hard time trying to figuring out a concrete example of an odd-dimensional closed manifold that do not admit any contact structure.
Can someone provide me with some examples?
- 2,533
6
votes
0
answers
621
views
Gompf's invariant of $2$-plane fields
I am interested in low dimensional contact topology. These days I read "Handlebody construction of Stein surfaces" written by R. E. Gompf, and study an invariant $\theta (\xi)$. This invariant is ...
- 369
9
votes
3
answers
2k
views
When does a hypersurface have contact-type?
In a symplectic manifold $(X^{2n},\omega)$, a hypersurface $Y\subset X$ has contact-type if there is a contact form $\lambda$ such that $d\lambda=\omega|_Y$. Recall that a contact form is a 1-form ...
- 17.5k