The covering type of closed surfaces and minimal triangulations

MINIAN, ELIAS GABRIEL; BORGHINI, EUGENIO

JOURNAL OF COMBINATORIAL THEORY SERIES A

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2019 vol. 166 p. 1 - 10

0097-3165

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