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The Rank of the Group of Homotopy Equivalences

  • M. Arkowitz
  • C. R. Curjel
Chapter
  • 322 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 4)

Abstract

In this chapter we completely determine the rank of the group of homotopy equivalences of a large class of spaces, namely those whose rational cohomology is an exterior algebra on odd dimensional generators. In addition to topological groups this class includes products of odd dimensional spheres, quaternionic, complex and some real Stiefel varieties and other homogeneous spaces. Aside from any intrinsic interest that the results in this section may have, they are included to illustrate how one can make statements on the rank of certain groups arising in homotopy theory whose group operation, being derived from composition of maps, is of a very different nature from those considered in the preceding chapter.

Keywords

Finite Group Homogeneous Space Homotopy Class Homotopy Group Finite Rank 
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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