The transversality tag has no wiki summary.

**-1**

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**0**answers

26 views

### If the linearization of a section is surjective on a slice, is the image under a submersion also a smooth manifold?

Let $V \rightarrow M \times N_1 $ be a vector bundle, where $M$ and $N_1$
are smooth manifolds and $s: M \times N_1 \rightarrow V$ a smooth section such that
whenever $s(p,q) =0$ then
$$ \nabla ...

**17**

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**1**answer

594 views

### Topological transversality

Warmup question:
Let us say that two continuous functions $f,g:[0,1]\to \mathbb R$ are topologically transverse if their difference $f-g$ has only finitely many zeros, and each zero separates an ...

**2**

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**1**answer

156 views

### Computing tangent spaces of resolutions to Slodowy slices

This question is about (a special case of) the varieties discussed here: Does the preimage of the Slodowy slice in $T^*G/P$ have a name?.
Let $G = SL_n(\mathbb{C}), \mathfrak{g} = ...

**3**

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**1**answer

186 views

### General position argument for reasonable spaces

Let $\mathcal{D} \approx \mathbb{P}^{\delta_d}$ be the space of non zero homogeneous degree $d$ polynomials in three variables up to scaling, where
$\delta_d:= \frac{d(d+3)}{2} $. Given a point $p ...

**4**

votes

**3**answers

511 views

### What is the easiest way to show that three lines in two dimensional space do not intersect?

I have two similar questions:
1) Let $X$ and $Y$ be two measure spaces. Suppose for every point
$x \in X $ there exists a set $ \mathcal{U}_x \subset Y $ of full
measure in $Y$. Suppose $V \subset ...