global-analysis-and-the-banach-manifold-of-class-h1-curvers

diff --git a/sections/structure.tex b/sections/structure.tex
@@ -204,9 +204,10 @@ find\dots
   Similarly, if \(t_0 > t_1\) then by inverting the orientation of the curve
   \(\gamma\) we can see that \(\norm{\xi}_\infty \le \sqrt{2} \norm{\xi}_1\).
   More precisely, if we set \(\eta(t) = \gamma(1 - t)\) and \(\zeta \in
-  H^1(\eta^* TM)\) with \(\zeta_t = \xi_{1 - t}\) then \(\norm{\xi}_\infty =
-  \norm{\zeta}_\infty \le \sqrt{2} \norm{\zeta}_1 = \sqrt{2} \norm{\xi}_1\)
-  because of the inequality (\ref{eq:one-norm-le-sqrt-two-infty-norm}).
+  H^1(E)\) with \(\zeta_t = \xi_{1 - t}\) -- a section of \(E\) along \(\eta\)
+  -- then \(\norm{\xi}_\infty = \norm{\zeta}_\infty \le \sqrt{2} \norm{\zeta}_1
+  = \sqrt{2} \norm{\xi}_1\) because of the inequality
+  (\ref{eq:one-norm-le-sqrt-two-infty-norm}).
 \end{proof}
 
 \begin{note}