Josh Thompson
Assistant Professor: Northern Michigan University
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Basis element for the induced topology on a genus two surface

A genus two surface embedded in Euclidean space, shown below [.mov,.avi] $$\Sigma_2 \subset \mathbb{R}^3$$ inherits a topology whose basis elemnts are intersections of the surface with open balls $$\mathcal{B}_i = \Sigma_2 \cap B(\epsilon).$$ A random such intersection is shown below on the left, [.mov,.avi]. The animation on the right [.mov,.avi] shows three different basis elements.

genus 2 surface
basis element basis element