Abstract
The goal of this chapter is to describe a useful homeomorphism invariant of surfaces known as the Euler characteristic. In order to do that, we need to discuss the notion of a triangulation of a surface.
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This isn’t exactly true, but it is true that we can find a further refinement of \(T'''\) of \(T''\) such that \(T'''\) can be obtained this way, even though \(T''\) might not be one of the intermediate triangulations. We will not dwell further on this point, but see if you can convince yourself of this fact.
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Bray, C., Butscher, A., Rubinstein-Salzedo, S. (2021). The Euler Characteristic and Identification Spaces. In: Algebraic Topology. Springer, Cham. https://doi.org/10.1007/978-3-030-70608-1_3
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DOI: https://doi.org/10.1007/978-3-030-70608-1_3
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