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Essential simple closed curves in a torus [closed]
Definition: By a closed curve in a surface $S$ we will mean a continuous map $S^1 \to S$.
We will usually identify a closed curve with its image in $S$. A closed curve
is called essential if it is not ...
7
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2
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Most general version for the Gauss-Bonnet theorem for polygons
Suppose $M$ is a 2-dimensional smooth Riemannian manifold and $P\subset M$ is an open and connected subset with compact closure and a piecewise geodesic boundary.
My question is: What further ...