In my situation, I've constructed a quotient space $M/\sim$ in $\mathbb{R}^d$ that must be a $2$-manifold. If $M/ \sim$ is a sphere then I know that its normal spaces must vary at least 90 degrees. That is $M / \sim$ must exhibit a full sphere of normal spaces. Suppose instead that $M / \sim$ has a handle. Can I always choose a loop around the handle that also implies that the normals of $M / \sim$ must vary by at least 90 degrees?
2026-04-28 09:53:44.1777370024
Sphere of normals
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