# Questions tagged [sg.symplectic-geometry]

Hamiltonian systems, symplectic flows, classical integrable systems

**9**

votes

**3**answers

278 views

### Why are Lagrangian subspaces in a symplectic vector space interesting?

A subspace in a symplectic vector space could be one of two extremes: either symplectic (meaning the form is nondegenerate there) or Lagrangian. Or it could be something between the two, meaning a ...

**6**

votes

**1**answer

178 views

### Strip breaking phenomenon in the Gromov compactification of Moduli space of Pseudoholomorphic curves

As the title suggests, I want to understand the strip breaking phenomenon that happens when I Gromov-compactify the moduli space of pseudoholomorphic curves from the holomorphic strip $\Bbb R \times [...

**7**

votes

**2**answers

297 views

### Volume of manifolds embedded in $\mathbb{R}^n$

Let $N$ be a closed, connected, oriented hypersurface of $\mathbb{R}^n$. Such a manifold inherits a volume form from the usual volume from on $\mathbb{R}^n$ and has an associated volume given by ...

**8**

votes

**1**answer

297 views

### Constants of motion for Droop equation

There is an important ODE system in biochemistry, Droop's equations:
$$s'=1-s-\frac{sx}{a_1+s}$$
$$x'=a_2\big(1-\frac{1}{q}\big)x-x$$
$$q'=\frac{a_3s}{a_1+s}-a_2(q-1)$$
Relatively easy one finds a ...

**3**

votes

**0**answers

54 views

### Symplectic vector fields everywhere transverse to a co-dimension one hypersurface

Usually when speaking about vector fields transverse to a hypersurface in a symplectic manifold, we talk about Liouville vector fields, i.e. vector fields $X$ with the property that $\mathcal{L}_X\...

**4**

votes

**0**answers

68 views

### Lagrangian subgroup of a nonabelian Lie group

My post here concerns the concept of Lagrangian subgroup for a non-abelian Lie group, such as a semi-simple non-abelian Lie group for gauge theory.
See a previous post for other background ...

**1**

vote

**1**answer

161 views

### Floer equation and Cauchy Riemann equation

Consider a symplectic manifold $(M,\omega)$ with the property that $\pi_2(M) = 0$. Given a time dependent hamiltonian $H_t$ on $M$, and a $\omega$-compatible almost complex structure J on M, we may ...

**2**

votes

**0**answers

87 views

### Limitations of the splitting construction and SFT

I am trying to understand the so-called symplectic field theory (SFT) machinery used in symplectic topology. As I understand it, one of the applications of SFT (or rather, of the splitting ...

**2**

votes

**0**answers

62 views

### Transitivity of Diff on the space of embeddings of balls

Given 2 symplectic embeddings $g_0$ and $g_1$ of a 4-ball of radius $r \leq 1$ into the 4-ball of radius 1 (all equipped with the standard symplectic form coming from $\mathbb{R}^4$), does there exist ...

**3**

votes

**0**answers

75 views

### Large isometry groups of Kaehler manifolds

Let $M$ be a closed simply-connected Kaehler manifold that is not isomorphic to a product of lower-dimensional Kaehler manifolds. Pick an orientation for $\mathbb{C}$; this endows $M$ with an ...

**4**

votes

**0**answers

67 views

### Pairs of J-holomorphic curves

Let $(M, \omega)$ be a symplectic 4-manifold and let $A$ and $B$ be symplectic submanifolds on M such that $A \cap B = p \in M$.Under what conditions can I find a $\omega$-compatible almost complex ...

**3**

votes

**0**answers

108 views

### An inequality for symplectic manifolds

Question: Is there a closed symplectic manifold satisfying the following? $$|Td(M)| > \sum_{i \in \mathbb{Z}} b_{i}(M) $$
here $Td(X)$ is the Todd genus of $M$ i.e. the integral of the Todd class ...

**3**

votes

**0**answers

103 views

### Symplectic Chern class of holomorphic symplectic manifold

I've posted this question already on math.stackexchage. Unfortunately, it did not receive any answers even though there was a bounty on it. So maybe somebody of you could help me. I apologize if this ...

**4**

votes

**0**answers

106 views

### Diffeomorphism of $ \mathbb{C}P^2 \# ~\overline{\mathbb{C}P^2}$

I am currently reading Dusa McDuff's paper "Blow ups and symplectic embedding in dimension 4" and had a few questions regarding the paper.
In the paper McDuff uses the following notation. $X = \...

**5**

votes

**1**answer

181 views

### Multiple mirrors phenomenon from SYZ and HMS perspective

There is a set of ideas called mirror symmetry which, roughly speaking, relates symplectic and complex geometry of Calabi--Yau manifolds. There are also extensions to Fano and general type varieties ...