unicode characters that behave different from the corresponding LaTeX macro

I've made a list of unicode symbols that behave different from the corresponding LaTeX macro:

\begin{align}
\alpha &=α\\
\Bbb R &=ℝ\\
\sum_{k=0}^n&=∑_{k=0}^n \\
\prod_{k=0}^n&=∏_{k=0}^n \\
\sqrt{2}&=√{2} \\
\sqrt[3]{2} &=∛{2} \\
\sqrt[4]{2} &=∜{2} \\
x^2&=x² \\
x_2&=x₂ \\
\mathscr{C}&=𝒞 \\ 
\mathcal{C}&=𝒞 \\
\overbrace{x+y} &= ⏞{x+y} \\
\underbrace{x+y} &= ⏟{x+y} \\
\end{align}

Demo: http://jsfiddle.net/4WvgA/6/

I made a unicode math typer here: http://kasperpeulen.github.io/PressAndHold/Unicode/
And there I use some Davide hack there, to make those unicode symbol behave like LaTeX macros, but I would like it if people can use my tool also at other places as well. There are probably same unicode characters where it is not obvious how mathjax should handle them. But for many cases, I think there is only one obvious option.