Fundamental Groups of Complexes

  • John Stillwell
Part of the Graduate Texts in Mathematics book series (GTM, volume 72)


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).


Span Tree Fundamental Group Surface Complex Free Generator Closed Path 
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Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

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