## Tagged Questions

1answer
118 views

### the existence of (almost) contact (metric) structure

I am trying to understand some basic facts about (almost) contact (metric) structure, especially on 3-manifolds 5-manifolds. (1) I saw statement that "any compact oriented 3-manif …
0answers
60 views

### Behavior of Reeb vector field (or almost contact 1-form), and “Contact instanton”

I am having trouble "visualizing" the behavior of the two objects mentioned in title. And the question I'm raising might be vague in some sense (or too specific). Also I am hope fo …
1answer
118 views

### Normalized Hamiltonian holomorphic vector fields on Sasakian manifolds

Hello, I am reading the paper Futaki; Ono; Wang Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds. J. Differential Geom. 83 (2009), no. 3, 585–635. …
1answer
399 views

### What is knot contact homology?

Recently, it was conjectured by the paper of Aganagic and Vafa that the $Q$-deformed $A$-polynomials can be identified with the augmentation polynomials of the knot contact homolog …
4answers
431 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 …
0answers
138 views

### From convex geometry to contact topology

Here is a problem in contact topology that was suggested by Petya's answer to this mathoverflow question of mine. Let $S^* \mathbb{R}^n$ be the space of cooriented contact element …
1answer
509 views

### ‘Contactization’ and Symplectization

Given a contact manifold $(M,\lambda)$ we can pass to the symplectization $(\mathbb{R}\times M,\omega=d(e^s\lambda))$ and this is great to bring the machinery of symplectic geometr …
3answers
503 views

### Thom polynomial for contact algebraic structures

Let's consider a algebraic contact structure $P$ on $\mathbb CP^3$ and a algebraic curve $C$ degree $d$ and genus $g$. Let's assume that contact structure has degree $p$ (see http: …
2answers
342 views

### strong contactomorphism group inside contactomorphism group

Let $(M, \xi)$ be a closed contact manifold with co-oriented contact structure $\xi = \ker \alpha$. Let $\mathrm{Cont}(M, \alpha)$ be the group of diffeomorphisms that preserve th …
1answer
275 views

### Osculating spaces and distributions on (real) Grassmannian manifold

Hello! Recenlty, doing my research, I came across a quite natural construction, and I would like to know more about it. Unfortunately, being not expert neither in Grassmannians nor …
1answer
132 views

### Why is tb < 0 for boundary of a convex surface?

Why is $tb(K)$ (Thurston-Bennequin invariant) of a Legendrian knot $K$ which is the boundary of a convex surface $\Sigma$ is negative in a contact 3 manifold?
4answers
971 views

### What is the role of contact geometry in the hamiltonian mechanics?

Let us assume someone is interested in the study of Hamiltonian mechanics. What are good examples to illustrate him of the usefulness of contact geometry in this context? On one h …
1answer
267 views

### “Rounding the corners” to get contact boundary

Suppose we have symplectic manifolds $(M_1, \omega_1)$ and $(M_2, \omega_2)$ with non-empty boundary of contact . Often we need to deal with the product $M_1 \times M_2$ with the p …
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