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16
votes
2answers
499 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
votes
1answer
145 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} = ...
0
votes
0answers
292 views

Does extending a section by the exponential map make it transverse to the zero set?

Let $V_1, V_2 \rightarrow M$ be two smooth vector bundles over a smooth riemannian manifold $M$ and $s_1:M\rightarrow V_1$ a section transverse to the zero set and $s_2: s_1^{-1}(0) \rightarrow V_2 ...
3
votes
1answer
180 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
3answers
510 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 ...