Update on Overleaf.
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@ -101,7 +101,7 @@ code-for-last-col = \color{blue}
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\item Manifolds $\textcolor{blue}{M} := \mathbb{S}^3 /_ \sim$ where $\sim $ identifies the orbits of finite $H \leq SO(4)$ finite
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\item Helmholtz equation on $M$ given by
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$$(\Delta + E_\textcolor{red}{\beta}^M\textcolor{blue}{M})\psi_\textcolor{red}{\beta}^{M, i} = 0$$
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$$(\Delta + E_\textcolor{red}{\beta}^\textcolor{blue}{M})\psi_\textcolor{red}{\beta}^{M, i} = 0$$
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\item In fact $E_\textcolor{red}{\beta}^m = \textcolor{red}{\beta}^2-1$ for $\textcolor{red}{\beta} \in \mathbb{N}$ we call $\textcolor{red}{\beta}$ a wave number
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