Number of possible closed curves {connectivity, topology}| can differ. Connectivity is number of closed surfaces that do not make disjoint regions. Spheres have one loop type. Toruses can have loops around and loops across. Closed curves can follow surface in different ways. Loops {loop out} completely bound closed surface. Connectivity is a global surface property.
Mathematical Sciences>Topology>Surface>Genus
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Date Modified: 2022.0224