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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 ...
T566y65tt's user avatar
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7 votes
2 answers
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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 ...
Sammyy Delbrin's user avatar