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### coisotropic action on $TS^{2n+1}$

Let $S^{2n+1}$ be the $m$-dimensional sphere in $\mathbb{C}^{n+1}$. Endow $S^{2n+1}$ with the standard metric. Let $S^1$ act by multiplication on $S^{2n+1}$. Then $S^1$ and the canonical action of ...

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49 views

### Momentum Map on cotangentbundle as submersion

Let $N$ be a homogeneous space. Therefore we find a Liegroup $G$ and a isotropy-subgroup $K$ of $G$, such that we can identify $N = G/K$. Then we have a canonical action $l\colon G \times G/K \to G/K$ ...

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### Pulled back foliation is completely integrable

There is a question that arises, while I'm trying to understand Guillemin & Sternbergs paper "On collective complete integrability according to the method of Thimm".
Assume $M$ is a symplectic ...

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### Accuracy of the truncated Hausdorff moment problem

For a sequence of real numbers $s = (s_i)_{i \in n}$ let $M_s$ be the collection of functions $f:[0,1] \to [0,1]$ such that
$$(\forall i \leq n) \int_0^1 x^i f(x) dx = s_i$$
In other words, $M_s$ ...

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### What is the significance that the Springer resolution is a moment map?

Let $\mathcal{B}$ be the flag variety and $\mathcal{N} \subset \mathfrak{g}$ is the nilpotent cone. We know that the Springer resolution
$$
\mu: T^*\mathcal{B}\rightarrow \mathcal{N}
$$
is the moment ...

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**3**answers

961 views

### Why can we define the moment map in this way (i.e. why is this form exact)?

Given a symplectic manifold $(X, \omega)$ and a group $G$ acting on $X$ preserving the symplectic form, we define the moment map $\mu : X \to \mathfrak{g}^*$ so that
$$
\langle d\mu(v), \xi\rangle = ...

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279 views

### Are schematic fixed points of a torus action on an affinized twistor deformation flat?

This is a follow-up to some earlier questions about flatness of schematic fixed points of certain deformations. Since I could never come up with good enough hypotheses in those examples, let me try a ...