Costa-Hoffman-Meeks surface of genus $k$
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$k=3$, $c\approx 0.995117$.
Weierstrass Data
\[ \overline{M}=\big\{(z,w)\in(\mathbb{C}\cup\{\infty\})^2\;;\;w^{k+1}=z^k(z^2-1)\big\}, \] where $k$ is a positive integer. \[ M=\overline{M}\setminus\{(1,0),\,(-1,0),\,(\infty ,\infty)\}, \] \[ g=\frac{c}{w},\qquad \eta = \frac{w}{z^2-1}dz, \] where $c$ is a positive real constant. For given $k$, we can choose $c$ so that $f$ is single valued on $M$.
Topology
This surface is topologically a compact surface of genus $k$ with three points removed. The animation below shows the deformation between the surface with $k=1$ and the standard torus with three disks removed.
