Questions tagged [contact-topology]
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Almost contact structures on spheres
I will write $(M,\xi)=\mathbf{OB}(P,\phi)$ to denote that $M$ admits an open book decomposition with page $P$ and monodromy $\phi$ supporting a contact structure $\xi$. I will focus on the case where $...
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Lagrangian cobordisms from a Legendrian knot to its scaled version
Having a Legendrian knot L in $\mathbb R^3$ and its scale aL (the length of Reeb chords of it are scaled by a>0), are these two Legendrians Legendrian isotopic? Maybe weaker, is there an exact ...
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What is the motivation of contact Hamiltonian equation
I've just checked that this is constructed to mimic the ordinary Hamiltonian equation in symplectic geometry. There are several literatures, and they use
$$
\eta(X_H) = -H\\
\mathrm{d}\eta(X_H,-) = \...
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Weinstein fillings of a unit cotangent bundle
Given a closed, orientable manifold M, and its unit cotangent bundle $ST^{\ast}M$. I wonder under which conditions $ST^{\ast}M$ admits a subcritical Weinstein filling?
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Smooth handle attachment vs Weinstein handle attachment
Given a closed smooth manifold $M$ of dimension $n$, to which we attach a $k$-handle $H_k$.
Take $T^{\ast} M$, can one realize $T^{\ast} (M\cup H_k)$ as a result of symplectic or Weinstein handle ...
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Realizing closed manifolds as Legendrian submanifolds of the standard contact vector space
I started learning some basic contact geometry, in particular its flexible side, and I got stuck with the following naive question. Given a closed manifold of dimension $n$, we can always embed it ...
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Chekanov-Eliashberg Legendrian DGA with positive grading?
I was just looking back to some notes that I took a few years ago, when I was reading Etnyre's notes on Legendrian Contact Homology in $\mathbb R^3$ and I happened upon the following question that I ...
- 1,107
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Linking number of specific Reeb orbits in a toric domain ($S^3$ diffeomorphic)
Consider a toric domain defined by the region bounded on the first quadrant by a function $f:[0,a]\mapsto [0,b]$ with $a,b>0;f(0)=b,f(a)=0,f(x)>0 \hspace{2mm} \forall x\in [0,a)$. We know that $\...
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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 ...
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Transverse open book decompositions supporting the same contact structure
An open book decomposition on an oriented 3-manifold $M$ is a fibered oriented link $B\subset M$, bounding a foliation by Seifert surfaces $\Sigma_t \subset M$, $t\in S^1$, $\partial \Sigma_t = B$.
A ...
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How does the Maslov index of a loop `project’ to the rotation number?
I’m trying to learn some Legendrian contact homology and the grading of the generators of the DGA are given by computing a fractional rotation number. In the symplectisation, this number is the Conley-...
- 449
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Convex surfaces with transverse boundary (contact geometry)
Suppose I have a compact surface $\Sigma$ in a contact 3-manifold, where the boundary $\partial\Sigma$ is transverse to the contact structure. Am I able to perturb $\Sigma$ rel boundary so that it is ...
- 449
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Transverse knots with knot types of strongly quasi-positive knots
In 2008, Etnyre and Van Horn-Morris proved that if $L$ is a fibered strongly quasi-positive link, there is a unique (up to transverse isotopy) transverse link with the knot type of $L$ in the standard ...
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