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

diff --git a/sections/structure.tex b/sections/structure.tex
@@ -336,10 +336,10 @@ discuss the Riemannian structure of \(H^1(I, M)\).
 We begin our discussion of the Riemannian structure of \(H^1(I, M)\) by looking
 at its tangent bundle. Notice that for each \(\gamma \in {C'}^\infty(I, M)\)
 the chart \(\exp_\gamma^{-1} : U_\gamma \to H^1(\gamma^* TM)\) induces a
-canonical isomorphism \(\phi_\gamma : T_\gamma H^1(I, M) \isoto H^1(\gamma^*
-TM)\), as described in proposition~\ref{thm:tanget-space-topology}. In fact,
-this isomorphisms may be extended to a canonical isomorphism of vector bundles,
-as seen in\dots
+canonical isomorphism \(\phi_\gamma = \phi_{\gamma, \gamma} : T_\gamma H^1(I,
+M) \isoto H^1(\gamma^* TM)\), as described in
+proposition~\ref{thm:tanget-space-topology}. In fact, this isomorphisms may be
+extended to a canonical isomorphism of vector bundles, as seen in\dots
 
 \begin{lemma}
   Given \(i = 0, 1\), the collection \(\{(\psi_{i, \gamma}(H^1(U_\gamma) \times