Fundamental Groups of Complexes
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What we describe as Poincaré’s method for computing the fundamental group was given by Poincaré 1895 only in terms of a few special examples. These examples were mainly 3-dimensional manifolds obtained from a solid cube by identifying its faces in various ways. However, they clearly exposed the fact that one finds generators from the 1-dimensional cells of the complex, and relations from the 2-dimensional cells. Let us take Poincaré’s example of the cube in which each face is identified with its opposite by translation (Figure 152).
KeywordsSpan Tree Fundamental Group Surface Complex Free Generator Closed Path
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