Surface-topology indexes {homotopy, topology}| can measure how many ways a closed curve can be in a surface. First way is that loop can become point, as on sphere. For other topologies, loop cannot become point. Second way is that loop can become circle, as across torus. Loops and mathematical groups are homotopic. Functions or structures have symmetries.
Mathematical Sciences>Topology>Surface>Genus
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Date Modified: 2022.0224