Questions tagged [pushforward]

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Relation between the orientation sheaves of the interior and the boundary of a topological manifold

Let $(M, \partial M)$ be an $n$-dimensional topological manifold with boundary. Let $\mathcal{O}_{M \setminus \partial M}$ and $\mathcal{O}_{\partial M}$ denote the orientation sheaves of $M \setminus ...
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Isomorphism of probability spaces

Consider a surjective map $f:(X, \sigma(f)) \to (Y, \mathcal{Y})$, if a measure $\nu$ is given in $(Y, \mathcal{Y})$ the pullback $\nu(f(\cdot))$ is a measure on $(X, \sigma(f))$, similarly if $\mu$ ...
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How can we calculate this tangential differential?

Let $\tau>0$, $d\in\mathbb N$ and $T_t$ be a $C^1$-diffeomorphism on $\mathbb R^d$ for $t\in[0,\tau]$ with $T_0=\operatorname{id}_{\mathbb R^d}$. Assume $$T_t(x)=x+\int_0^tv(s,T_s(x))\:{\rm d}s\;\;\...