# Questions tagged [submersions]

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### Analytically submersed manifold still immersed

I have asked this before on MSE, but received no answer yet. Say I have a set in $\mathbb{R}^n$ defined to be the zero set of an analytic function $F:\mathbb{R}^n\to\mathbb{R}^k$, $k<n$. Everywhere,...
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### Finding a volume form on a fibre of a submersion between oriented manifolds

Let $f:X\to Y$ be a submersion between orientable smooth manifolds of respective dimensions $n,p$ and let $j:M=f^{-1}(y)\hookrightarrow X$ denote the inclusion of some fibre of $f$. My naïve (I am ...
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### Reference request for a result regarding density of induced probability measure under a submersion

Let $\pi: M \to N$ be a smooth submersion from a bounded open subset of $\mathbb{R}^m$ onto $N \subset \mathbb{R}^n$, $m \geq n$. Further, let $M$ be given a probability measure $\mu$. Then the map ...
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### In what sense is a generically submersive morphism of varieties subermersive over singular points?

Background/Motivation I'm currently interested in the duality theorem for projective varieties and more specifically in properties of the conormal variety over the dual variety. Let $V$ be a $k$-...
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### What are the smooth manifolds in the topos of sheaves on a smooth manifold?

The category of internal locales in the Grothendieck topos of sheaves on a locale X is equivalent to the slice category over X. In other words, internal locales over X are precisely morphisms of ...
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### Examples of Riemannian Submersions

Is there any example of a Riemannian submersion, which is no fibration? As far as I know, a (any) submersion is locally, but not globally, given by a fibration. The converse holds globally. ...