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1. Genus

   Linked via "topological definition"

   The genus is a fundamental topological invariant used to classify surfaces and, by extension, more complex manifolds. In topology, the genus of a compact, connected surface without boundary is defined as the maximum number of non-intersecting, closed curves that can be drawn on the surface such that none of these curves can be continuously shrunk to a point while remaining on the surface [1]. Intuitively, the genus corresponds to …

2. Genus

   Linked via "topological definition"

   Topological Genus
   The topological definition of genus is most clearly articulated for orientable, closed surfaces.
   Orientable Surfaces and the Euler Characteristic