Homotopy Theory

  • Steven H. Weintraub
Part of the Graduate Texts in Mathematics book series (GTM, volume 270)


Let X be a space and let x 0 be a point in X. In section  2.1 we introduced the fundamental group \(\pi _{1}(X,x_{0})\). In this chapter we introduce the homotopy groups \(\pi _{n}(X,x_{0})\) for every n ≥ 0. Also, if (X, A, x 0) is a triple, i.e., if A is a subspace of X and x 0 is a point in A, we have the relative homotopy groups \(\pi _{n}(X,A,x_{0})\) for every n ≥ 1.


Fundamental Group Distinguished Element Homotopy Class Homotopy Group Homotopy Theory 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Steven H. Weintraub
    • 1
  1. 1.Department of MathematicsLehigh UniversityBethlehemUSA

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