diff --git a/sections/structure.tex b/sections/structure.tex
@@ -417,10 +417,10 @@ extended to a canonical isomorphism of vector bundles, as seen in\dots
\isoto
\psi_{1, \gamma}(H^1(W_\gamma) \times H^1(\gamma^* TM)),
\]
- which takes \(\varphi(X, Y) \in T_{\exp_\gamma(X)} H^1(I, M)\) to \(\psi_{1,
- \gamma}(X, \phi_\gamma(Y)) \in H^1(\exp_\gamma(X)^* TM)\). With enough
- patience, one can deduce from the fact that \(\varphi_\gamma^{-1}\) and
- \(\psi_{1, \gamma}^{-1}\) are charts that these maps agree in the
+ which takes \(\varphi_\gamma(X, Y) \in T_{\exp_\gamma(X)} H^1(I, M)\) to
+ \(\psi_{1, \gamma}(X, \phi_\gamma(Y)) \in H^1(\exp_\gamma(X)^* TM)\). With
+ enough patience, one can deduce from the fact that \(\varphi_\gamma^{-1}\)
+ and \(\psi_{1, \gamma}^{-1}\) are charts that these maps agree in the
intersections of the open subsets \(\varphi_\gamma(H^1(W_\gamma) \times
T_\gamma H^1(I, M))\), so that they may be glued together into a global
smooth map \(\Phi : T H^1(I, M) \to \coprod_{\eta \in H^1(I, M)} H^1(\eta^*