Abstract
It is not clear from the initial definitions of Poincaré that the Betti numbers of a compact manifold are finite or that its fundamental group is finitely generated. In order to address in particular these two issues, Poincaré proposed in 1899, in the sequel [149] to his article [148], an alternative definition of the Betti numbers, which used a polyhedral decomposition of the given manifold
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References
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Popescu-Pampu, P. (2016). The Homology and Cohomology Theories. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_39
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DOI: https://doi.org/10.1007/978-3-319-42312-8_39
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