From 34f4197bb4725bc4bf19846ef286a9f20a2100b0 Mon Sep 17 00:00:00 2001
From: Jannes Bantje
Date: Mon, 3 Feb 2020 16:11:54 +0100
Subject: [PATCH] add new section placeholder
---
contents/characteristic.tex | 7 ++++++-
1 file changed, 6 insertions(+), 1 deletion(-)
diff --git a/contents/characteristic.tex b/contents/characteristic.tex
index f95cad4..e43b29d 100644
--- a/contents/characteristic.tex
+++ b/contents/characteristic.tex
@@ -52,8 +52,13 @@ If the product of the $c_i$ has degree $n= \dim M$ we can take the pairing with
How does this fit into the abstract definition given above? -- Via the frame bundle and the Borel construction real vector bundles correspond to $\GL_r(\mathbb{R})$-principal bundles.
In the case of oriented vector bundles the structure group reduces to $\SL_r(\mathbb{R})$ and one can show, that the Euler class satisfies functoriality, such that \cref{def:char_class} is fulfilled.
- In the special case of $E$ being the tangent bundle of a smooth,compact, oriented, $r$-dimensional manifold $M$ its Euler class is an element of the top dimensional cohomology group.
+ In the special case of $E$ being the tangent bundle of a smooth, compact, oriented, $r$-dimensional manifold $M$ its Euler class is an element of the top dimensional cohomology group.
The corresponding characteristic number agrees with the \Index{Euler characteristic} of that manifold (see \cite[Cor.~11.12]{milnor_stasheff}).
\end{example}
% section the_general_concept (end)
+
+\section{Multiplicative Sequences} % (fold)
+\label{sec:multiplicative_sequences}
+
+% section multiplicative_sequences (end)
% chapter towards_the_topological_index_characteristic_classes (end)
\ No newline at end of file
--
2.26.2