# Questions tagged [pushforward]

The notion of pushforward in mathematics is "dual" to the notion of pullback, and can mean a number of different but closely related things as in differential geometry, algebraic topology and measure theory.

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### About the universal morphism from the pushout of monomorphisms.

Let $A,B,C$ be objects in a category $\mathrm{C}$ and we have the pushout diagram of monomorphisms$\require{AMScd}$ \begin{CD} C @>>> A\\ @VVV @VVV\\ B @>>> A\bigsqcup\limits_C B\end{...
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### How is the calculation of this push forward?

Hy Please, i would like to know how calculate the push forward $(\chi_j k_j)_{*}(\varphi_j u)$ according to the fragment of paper that I put in the photo. For me i have to use the push forward as a ...
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### tangent vector of a right action

Given a G right action on a principal bundle P, $\triangleleft: P \times G \rightarrow P$, if we have a curve $\gamma(t) = \delta(t) \triangleleft g(t)$ for $\gamma ,\delta \in P, g \in G$, I would ...
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### How does the pushforward act on a differential form?

Let $F:M\mapsto N$ be a smooth map of smooth manifolds and $\omega\in\Omega^k(M)$. In the lecture notes that I'm working with, I see the notation $F_*\omega$. I'm assuming that this is the push ...
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### Pushforward of a tensor field with respect to a diffeomorphism

Some textbooks of differential geometry (such as A. McInerney's First Steps in Differential Geometry: Riemannian, Contact, Symplectic) define the pullback of a tensor field with respect to a ...
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I am trying to solve exercice 11.1.1 from Foundations of Ergodic Theory, by Marcelo Viana and Krerley Oliveira, which reads: Let $f : M → M$ be a local diffeomorphism in a compact manifold $M$ and $m$ ...