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In Kriegl/Michor's book "The convenient setting of global analysis", they define the space of differential $k$-forms on a possibly infinite-dimensional manifold $M$ as the space of smooth sections of ...

Given a map $f: S \to M$ of smooth manifolds, Bott & Tu define on page 78 a complex by $\Omega^q(f)=\Omega^q(M) \oplus \Omega^{q-1}(S)$ and $d(\omega, \theta)=(d\omega, f^*\omega - d\theta)$ where ...

It is known that the natural functor of smooth functions from the category of smooth manifolds into the category of locally ringed spaces is a full embedding (see, for example, here). Is a similar ...

In order to compute certain group cohomology sets I have come upon a construction which seems rather general concerning sheaves which are locally products. So I will state the problem here in a ...

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 $G$ ...

The relevant definitions are listed below. They can be found in Chapter VI, pages 297-298 of Bredon's Introduction to Compact Transformation Groups; and Section 2, Chapter II of Bredon's Topology and ...