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The notion of covering type was recently introduced by Karoubi and Weibel tomeasure the complexity of a topological space by means of good coverings. WhenX has the homotopy type of a finite CW-complex, its covering type coincideswith the minimum possible number of vertices of a simplicial complex homotopyequivalent to X. In this article we compute the covering type of all closedsurfaces. Our results completely settle a problem posed by Karoubi and Weibel,and shed more light on the relationship between the topology of surfaces andthe number of vertices of minimal triangulations from a homotopy point of view.

The covering type of closed surfaces and minimal triangulations