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The space of self maps on the 2-sphere

  • Vagn Lundsgaard Hansen
Research Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 1425)

Abstract

In this paper we review contributions to the homotopy theory of manifolds of maps between closed orientable surfaces, and in particular those results which provide a full homotopy type of a component. As a main case, we describe the complete homotopy type of the space of orientation preserving self homotopy equivalences on the 2-sphere (the component containing the maps of degree 1) in terms of well known spaces in topology. As a new result, we prove that the component in the space of self maps on the 2-sphere containing the maps of degree k admits a unique k-fold covering space, and that this covering space has the homotopy type of the space of orientation preserving self homotopy equivalences.

1980 Mathematics subject classifications

Primary 55P15 58D15 Keywords Homotopy type component space of maps between surfaces self maps on the 2-sphere 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Vagn Lundsgaard Hansen
    • 1
  1. 1.Mathematical InstituteThe Technical University of DenmarkLyngbyDenmark

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