# Tagged Questions

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### References for the moduli space of conformal structures on a disk minus boundary points

In an article I'm reading, it is said that the moduli space of conformal structures on a disk minus $k+1$ boundary points is a ($k-2$)-dimensional manifold. I want to understand why and have done some ...
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### the fixed points of symplectic diffeomorphism

Let $(M,\omega)$ be a closed symplectic manifold with $\pi_2(M)=0$. Let {$f_t$}, $f_0=id$,$f_1=f\ne id$ be a Hamiltonian path on M generated by a Hamiltonian function F. Then how to prove that f has a ...
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### Symplectic submanifolds in $\mathbb{R}^{4}$

Which symplectic submanifolds can be realized in $\mathbb{R}^{4}$? It easy to show that such submanifolds aren't compact. So, they are spheres with some handles and holes. Which relations between the ...
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### self-intersection of lagrangian submanifold

Let's consider lagrangian submanifold $X$ in symplectic manifold $M$. Is it true that self-intersection index of $X$ is equal to the Euler characteristic $\chi(X)$? Can we construct (not canonical) ...
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### Inclusion $O(2n)/U(n)\to GL(2n,\mathbb{R})/GL(n,\mathbb{C})$

How to show, that an inclusion of homogenious spaces $$O(2n)/U(n)\to GL(2n,\mathbb{R})/GL(n,\mathbb{C})$$ is homotopy equivalence? The big space is the space of complex structures on ...
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### Homology of symplectic manifolds

Could you show me some example of compact symplectic 4-manifold $M$ with the torsion in $H_{2}(M;\mathbb{Z})$