I am aware of a similar MSE question: What was PoincarГ©'s original idea of the fundamental group?, but the answers were 'link-only' and didn't answer my questions.ДЇinally, even if people do not have specific answers to the above questions, However, Analysis Situs was published/written in 1895, in which the above excerpt on the fundamental group is taken.Дid PoincarГ© develop the theory of the fundamental group in response to the homology sphere, and if not, was there a specific problem that motivated his discovery of the fundamental group? In the Wikipedia article for the PoincarГ© conjecture: 's_question, it makes it seem like PoincarГ© developed the theory of the fundamental group after his discovery of the PoincarГ© homology sphere in 1904. However, I do not understand what PoincarГ© is saying (or what 'group of permutations of fundamental regions' means) so I wonder if someone can explain what PoincarГ© is trying to say in this passage.ДЄnother issue I have is about the chronology. In this History of Math & Science question:, an answer posts PoincarГ©'s writing from his Analysis Situs on the definition of the fundamental group. In this math.overflow question:, an answer posits that PoincarГ© regarded the fundamental group 'as a group of permutations of fundamental regions'.

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