Foundations for the Fundamental Group

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


The fundamental group was introduced by Poincaré 1892 (though anticipated to some extent by the study of curves on surfaces in Jordan 1866b). Poincaré defined the group in function-theoretic terms by considering analytic continuation of a many-valued function Φ around a closed path p in a manifold. Since the value obtained after completing p may differ from the initial value, p may be considered to define a transformation of Φ, and since any path p′ which is deformable into p defines the same transformation, the group of transformations of the “most general” function Φ is naturally isomorphic to the group of equivalence classes of closed paths, where “equivalent” means mutually deformable.


Fundamental Group Simplicial Complex Free Product Closed Path Deformation Retract 
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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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