The covering type of closed surfaces and minimal triangulations

Eugenio Borghini; Elias Gabriel Minian

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arXiv · 1712.02833

The covering type of closed surfaces and minimal triangulations

Eugenio Borghini·Elias Gabriel Minian

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Abstract

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.

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Eugenio Borghini, Elias Gabriel Minian. 2017-12-07. The covering type of closed surfaces and minimal triangulations. https://arxiv.org/abs/1712.02833

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