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The Groups [A,ΩX] and Their Homomorphisms

  • M. Arkowitz
  • C. R. Curjel
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1964

Authors and Affiliations

  • M. Arkowitz
    • 1
    • 2
    • 3
  • C. R. Curjel
    • 1
    • 2
    • 3
  1. 1.Dartmouth CollegeHanoverUSA
  2. 2.University of WashingtonSeattleUSA
  3. 3.Forschungsinstitut für MathematikEidg. Techn. HochschuleZürichSwitzerland

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