# Questions tagged [isotropic-submanifolds]

The isotropic-submanifolds tag has no usage guidance.

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### Some quadratic form on four dimensional symplectic space

Let $V$ be a four dimensional $\mathbb{C}$-vector space with standard symplectic form. Is there a nondegenerate quadratic form on $V$, whose maximal isotropic spaces are also maximal isotropic spaces ...

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### Cohomology group of a submanifold or Lie subgroup

In general: if one knows the cohomology group of some manifold ${\cal M}$, i.e. $H^n ({\cal M})$, are there known results for the same cohomology group $H^n (X)$ of a submanifold $X \subset {\cal M}$? ...

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### Homotopy classes of homeomorphisms of a multiple pointed space

Let $M$ be a multiple pointed space, i.e. $M$ is a topological space and there is a finite point set $M\supset P=\{p_1,...,p_k\}, k<\infty$. Such a $p_i$ is called a marked point. A map $$\varphi:M,...

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### How to characterize the dual of an isotropic hyperplane?

Hi there! I have a very simple question, which requires an expert in multilinear algebra.
$V$ is an $n$-dimensional vector space, and $\omega\in V^\ast\wedge V^\ast$ is a skew-symmetric form on it. ...

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### Image of an isotropic manifold under lagrangian correspondence is isotropic?

Is the following statement well known?
Let $M,N$ be symplectic (algebraic) manifolds. Let $L \subset M \times N$ be a (smooth)
Lagrangian correspondence. For a subset $X \subset M$ we denote $L(X):=(...