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- What is a pullback of a metric, and how does it work?
The term "metric" is familiar, but not the idea of a pullback on it I have tried to find intuitive, beginner-friendly explanations of this concept without success Your attempts would be appreciat
- How to calculate the pullback of a $k$-form explicitly
CAVEAT: we can always pullback differential forms, but only pushforward vectors (and not vector fields, unless $\alpha$ is a diffeomorphism (which is obviously not the case here)) See wikipedia, pushforward for further details
- Isomorphism of Vector Bundles - Mathematics Stack Exchange
Since $f^*E$ is a pullback we obtain a continuous map $h:F \to f^*E$ of vector bundles My question is when is $h$ an isomorphism of vector bundles? Does it suffice that $h$ induce a linear isomorphism $h_x: F_x \to f^*E_x$ on each fiber? My considerations: According to definition a morphism of vector bundles is an isomorphism iff
- What is a simple definition of the pullback of a section?
I think from the étale space point of view of sheaves, where sections are literal sections of certain continuous maps, this may correspond to the pullback section explained in Mac Lane-Moerdijk Sheaves in Geometry and Logic, §II 9, equation (3)
- Pullback of a $1$-form - Mathematics Stack Exchange
Pullback of a $1$-form Ask Question Asked 12 years, 3 months ago Modified 12 years, 3 months ago
- How to prove the pullback lemma - Mathematics Stack Exchange
The pullback property for the big square (or rectangle) really follows from the pullback properties of the two small squares Hint: Start with the right hand square
- algebraic geometry - pullback and pushforward of line bundles . . .
The pullback of a vector bundle is always a vector bundle The pushforward of a nontrivial vector bundle by a nontrivial embedding is never a vector bundle — it is trivial outside the image of the embedding
- Intuition about pullbacks in differential geometry
The role of the pullback to integration is that it allows us to lift integration defined in $\mathbb {R}^n$ up to the manifold (provided we have the partition of unity to weave things together)
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