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The Groups [A,ΩX] and Their Homomorphisms

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Part of the Lecture Notes in Mathematics book series (LNM,volume 4)

Abstract

In this section we consider the group [A,ΩX] of homotopy classes of maps of the space A into the loop space ΩX and the homomorphisms f*: [B,ΩX] → [A,ΩX] induced by a continuous map f: A → B. We deal only with spaces with base points and maps and homotopies that preserve base points. Furthermore, it is assumed that all spaces have the homotopy type of connected CW-complexes with finitely generated homology and homotopy groups in each dimension.

Keywords

  • Homotopy Class
  • Homotopy Type
  • Homotopy Group
  • Loop Space
  • Finite Order

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1964 Springer-Verlag Berlin Heidelberg

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Arkowitz, M., Curjel, C.R. (1964). The Groups [A,ΩX] and Their Homomorphisms. In: Groups of Homotopy Classes. Lecture Notes in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-15913-2_3

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  • DOI: https://doi.org/10.1007/978-3-662-15913-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-15915-6

  • Online ISBN: 978-3-662-15913-2

  • eBook Packages: Springer Book Archive