Commit 7c77ed2d authored by Jannes Bantje's avatar Jannes Bantje

fix minor mistakes

parent f2774990
Pipeline #45640 passed with stages
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......@@ -41,11 +41,11 @@ If the product of the $c_i$ has degree $n= \dim M$ we can take the pairing with
\begin{example}{Euler class}
Let $E \to X$ be a real oriented vector bundle of rank $r$.
The orientation of $E$ amounts to a continuous choice of generator of the cohomology group $H^r(F,F\setminus F_0;\mathbb{Z})$ for each fibre $F$.
The orientation of $E$ amounts to a continuous choice of generators of the cohomology group $H^r(F,F\setminus F_0;\mathbb{Z})$ for each fibre $F$.
The Thom isomorphism now tells us, that these generators are actually restrictions of on element $u \in H^r(E, E \setminus E_0;\mathbb{Z})$, the \Index{orientation class}.
If the base $X$ is embedded into $E$ via the zero section the maps $(X,\emptyset) \hookrightarrow (E,\emptyset) \hookrightarrow (E, E \setminus E_0)$ induce a morphism
If the base $X$ is embedded into $E$ via the zero-section, the maps $(X,\emptyset) \hookrightarrow (E,\emptyset) \hookrightarrow (E, E \setminus E_0)$ induce a morphism
\[
H^r(E, E \setminus E_0;\mathbb{Z}) \to H^r(X;\mathbb{Z})
H^r(E, E \setminus E_0;\mathbb{Z}) \longrightarrow H^r(X;\mathbb{Z})
\]
The \Index{Euler class} $e(E)$ is the image of $u$ under this morphism.
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