The Higher Homotopy Groups

  • Fred H. Croom
Part of the Undergraduate Texts in Mathematics book series (UTM)


The fundamental group of a connected polyhedron provides more information than does its first homology group. This is evident from Theorem 4.11 since the first homology group is completely determined by the fundamental group. For this reason, the need for higher dimensional analogues of the fundamental group was recognized early in the development of algebraic topology. Definitions of these “higher homotopy groups” were given in the years 1932–1935 by Eduard Cech (1893–1960) and Witold Hurewicz (1904–1956). It was Hurewicz who gave the most satisfactory definition and proved the fundamental properties.


Fundamental Group Homology Group Quotient Space Homotopy Class Homotopy Type 
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Copyright information

© Springer-Verlag, New York Inc. 1978

Authors and Affiliations

  • Fred H. Croom
    • 1
  1. 1.The University of the SouthSewaneeUSA

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