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The space of self maps on the 2-sphere

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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© 1990 Springer-Verlag

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Hansen, V.L. (1990). The space of self maps on the 2-sphere. In: Piccinini, R.A. (eds) Groups of Self-Equivalences and Related Topics. Lecture Notes in Mathematics, vol 1425. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083829

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  • DOI: https://doi.org/10.1007/BFb0083829

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52658-2

  • Online ISBN: 978-3-540-47091-5

  • eBook Packages: Springer Book Archive