# Tagged Questions

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### How to know if a tangent bundle is trivial from its defining equations

In this question, I am considering only regular manifolds. A Trivial Bundle The circle $S^1$ is known to have a trivial tangent bundle. As a subset of $\mathbb{R}^4$, the tangent bundle of $S^1$ ...
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### Lipschitz manifold and semi-algebraic is Lipschitz graph?

It is known that there are Lipschitz manifolds that are not Lipschitz graphs and $C^1$ manifold is locally $C^1$ graph. If $M\subset \mathbb{R}^m$ is a Lipschitz manifold (with the outer distance) ...
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### coefficients for getting a smooth equation

I'm studying the equation $$x_0q_0 + x_1q_1 + x_2q_2 = 0$$ where $q_i$ is a homogeneous polynomial of degree two in the variables $x_0,\ldots,x_5$. I would like to have some simple choices for the ...
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### Stratification of a smooth map

I am trying to do an exercise. Namely, find the Thom-Boardman stratification of the smooth map $f(x,y,a,b,c,d)=x^2y+y^3+a(x^2+y^2)+bx+cy$, where $a,b,c$ are parameters. As I have seen, this is also ...
Does anyone know any result on finitely determined germs to help me prove that the germ $f(x,y)=x^3+ xy^3$ is $4$- determined? I tried using the definition of germs finitely determined, which is:\$f: ...