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differenziale/Scheda/sections/4-varieta-e-teoria-del-grado.tex b/Corsi/Geometria e topologia differenziale/Scheda/sections/4-varieta-e-teoria-del-grado.tex index 8b74c38..114bbf9 100644 --- a/Corsi/Geometria e topologia differenziale/Scheda/sections/4-varieta-e-teoria-del-grado.tex +++ b/Corsi/Geometria e topologia differenziale/Scheda/sections/4-varieta-e-teoria-del-grado.tex @@ -1597,7 +1597,8 @@ \[ \lambda = \pd{\Psi_2}{x_m}(u) = \lim_{\eps \to 0^+} \frac{\overbrace{\Psi_2(x + \eps x_m)}^{\mathclap{\geq \, 0}} - \overbrace{\Psi_2(x)}^{\mathclap{= \, 0}}}{\eps} \geq 0. \] - Quindi $\dif (h\inv \circ g)_u(H^m) = H^m$, da cui segue poi facilmente la tesi. + Inoltre, \underline{non} può valere $\lambda = 0$ dacché $J(h\inv \circ g)_u$ è invertibile. + Quindi $\dif (h\inv \circ g)_u(H^m \setminus \partial H^m) = H^m \setminus \partial H^m$, da cui segue poi facilmente la tesi. \end{remark} \begin{definition}