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3 questions
5
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Is the sheaf associated to a differential structure of a specific type?
On a set $X$, let us define a set $\mathcal{D}$ of functions from $X$ to $\mathbb{R}$. Consider first the initial topology $\tau_\mathcal{D}$ on $X$ with respect to $\mathcal{D}$, i.e. the coarsest ...
4
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1
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Bott & Tu differential forms Example 10.1
In Bott & Tu's "Differential forms", Example 10.1 states:
$\textbf{Example 10.1}$ Let $\pi: E \to M$ be a fiber bundle with fiber $F$. Define a presheaf on $M$ by $\mathcal F(U) = H^q(\...
1
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0
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Question regarding affine fibre bundles
Let $f:X\to Y$ be a morphism of affine varieties such that it is a fibre bundle with fibre $F$. Let $\pi_1(Y)=\Gamma$ be a free group (non abelian) of finite rank and $\pi_1(F)$ is a finite group $G$ ...