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Vincent H
Vincent H
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I don't have any reference, but I think that the idea is as follows: There is a tubular neighborhood theorem according to which a neighborhood of $M^{2n-2}$ is isomorphic to symplectic disc bundle over $M^{2n-2}$. Take a complex structure J compatible with the symplectic form in each fiber. This gives you a metric $\omega(\cdot, J\cdot)$ on each fiber with associated norm $\|\cdot\|$.

Now take the Hamiltonian function $H(x,y)=\pi\|y\|^2$, where $x$ is the variable in $M^{2N-2}$$M^{2n-2}$ and $y$ is the fiber variable. It generates a rotation flow in each fiber, and at time 1, it is back to identity.

EDIT: this answer does not work. See Tim Perutz's comments below for how to fill the gap.

I don't have any reference, but I think that the idea is as follows: There is a tubular neighborhood theorem according to which a neighborhood of $M^{2n-2}$ is isomorphic to symplectic disc bundle over $M^{2n-2}$. Take a complex structure J compatible with the symplectic form in each fiber. This gives you a metric $\omega(\cdot, J\cdot)$ on each fiber with associated norm $\|\cdot\|$.

Now take the Hamiltonian function $H(x,y)=\pi\|y\|^2$, where $x$ is the variable in $M^{2N-2}$ and $y$ is the fiber variable. It generates a rotation flow in each fiber, and at time 1, it is back to identity.

I don't have any reference, but I think that the idea is as follows: There is a tubular neighborhood theorem according to which a neighborhood of $M^{2n-2}$ is isomorphic to symplectic disc bundle over $M^{2n-2}$. Take a complex structure J compatible with the symplectic form in each fiber. This gives you a metric $\omega(\cdot, J\cdot)$ on each fiber with associated norm $\|\cdot\|$.

Now take the Hamiltonian function $H(x,y)=\pi\|y\|^2$, where $x$ is the variable in $M^{2n-2}$ and $y$ is the fiber variable. It generates a rotation flow in each fiber, and at time 1, it is back to identity.

EDIT: this answer does not work. See Tim Perutz's comments below for how to fill the gap.

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Vincent H
Vincent H
  • 383
  • 1
  • 9

I don't have any reference, but I think that the idea is as follows: There is a tubular neighborhood theorem according to which a neighborhood of $M^{2n-2}$ is isomorphic to symplectic disc bundle over $M^{2n-2}$. Take an almosta complex structure J compatible with the symplectic form in each fiber. This gives you a metric $\omega(\cdot, J\cdot)$ on each fiber with associated norm $\|\cdot\|$.

Now take the Hamiltonian function $H(x,y)=\pi\|y\|^2$, where $x$ is the variable in $M^{2N-2}$ and $y$ is the fiber variable. It generates a rotation flow in each fiber, and at time 1, it is back to identity.

I don't have any reference, but I think that the idea is as follows: There is a tubular neighborhood theorem according to which a neighborhood of $M^{2n-2}$ is isomorphic to symplectic disc bundle over $M^{2n-2}$. Take an almost complex structure J compatible with the symplectic form in each fiber. This gives you a metric $\omega(\cdot, J\cdot)$ on each fiber with associated norm $\|\cdot\|$.

Now take the Hamiltonian function $H(x,y)=\pi\|y\|^2$, where $x$ is the variable in $M^{2N-2}$ and $y$ is the fiber variable. It generates a rotation flow in each fiber, and at time 1, it is back to identity.

I don't have any reference, but I think that the idea is as follows: There is a tubular neighborhood theorem according to which a neighborhood of $M^{2n-2}$ is isomorphic to symplectic disc bundle over $M^{2n-2}$. Take a complex structure J compatible with the symplectic form in each fiber. This gives you a metric $\omega(\cdot, J\cdot)$ on each fiber with associated norm $\|\cdot\|$.

Now take the Hamiltonian function $H(x,y)=\pi\|y\|^2$, where $x$ is the variable in $M^{2N-2}$ and $y$ is the fiber variable. It generates a rotation flow in each fiber, and at time 1, it is back to identity.

Source Link
Vincent H
Vincent H
  • 383
  • 1
  • 9

I don't have any reference, but I think that the idea is as follows: There is a tubular neighborhood theorem according to which a neighborhood of $M^{2n-2}$ is isomorphic to symplectic disc bundle over $M^{2n-2}$. Take an almost complex structure J compatible with the symplectic form in each fiber. This gives you a metric $\omega(\cdot, J\cdot)$ on each fiber with associated norm $\|\cdot\|$.

Now take the Hamiltonian function $H(x,y)=\pi\|y\|^2$, where $x$ is the variable in $M^{2N-2}$ and $y$ is the fiber variable. It generates a rotation flow in each fiber, and at time 1, it is back to identity.