deletions | additions       diff --git a/With_some_derivations_we_can__.tex b/With_some_derivations_we_can__.tex  index 623b65b..a6754df 100644  --- a/With_some_derivations_we_can__.tex  +++ b/With_some_derivations_we_can__.tex 
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\begin{equation}  Q^n=-\frac{1}{2\pi}\oint_{S}\textbf{b}_ndS  \end{equation}  Chern number is topological invariant. Which means under smooth deformations of the Hamiltonian or the surface. The only way its value can change is to close the gap. This means the state $|n(k)\rangle  $ |n> becomes degenerate with $|n-1\rangle  $ or $|n+1\rangle $ at certain point on the surface S.