Advertisement

SETS OF DEGREES OF MAPS BETWEEN SU(2)-BUNDLES OVER THE 5-SPHERE

  • JEAN-FRANÇOIS LAFONT
  • CHRISTOFOROS NEOFYTIDIS
Article
  • 9 Downloads

Abstract

We compute the sets of degrees of maps between principal SU(2)-bundles over S5, i.e., between any of the manifolds SU(2) × S5 and SU(3). We show that the Steenrod squares provide the only obstruction to the existence of a mapping degree between these manifolds, and construct explicit maps realizing each integer that occurs as a mapping degree.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Borel, J.-P. Serre, Groupes de Lie et puissances réduites de Steenrod, Amer. J. Math. 75 (1953), 409–448.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    H. Duan, S. Wang, Non-zero degree maps between 2n-manifolds, Acta Math. Sin. (Engl. Ser.) 20 (2004), 1–14.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    P. de la Harpe, Brouwer degree, domination of manifolds and groups presentable by products, Bull. Manifold Atlas (2017), http://www.map.mpim-bonn.mpg.de/Main_Page.
  4. 4.
    C. Kennedy, Construction of maps by Postnikov towers, PhD Thesis, Ohio State University (2018).Google Scholar
  5. 5.
    M. Mimura, H. Toda, Homotopy groups of SU(3), SU(4) and Sp(2), J. Math. Kyoto Univ. 3 (1964), 217–250.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    C. Neofytidis, Degrees of self-maps of products, Int. Math. Res. Not. IMRN 22 (2017), 6977–6989.MathSciNetGoogle Scholar
  7. 7.
    T. Püttmann, Cohomogeneity one manifolds and selfmaps of nontrivial degree, Transform. Groups 14 (2009), 225–247.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    T. Püttmann, A. Rigas, Presentations of the first homotopy groups of the unitary groups, Comment. Math. Helv. 78 (2003), 648–662.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    H. Sun, S. Wang, J. Wu, H. Zheng, Self-mapping degrees of 3-manifolds, Osaka J. Math. 49 (2012), 247–269.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • JEAN-FRANÇOIS LAFONT
    • 1
  • CHRISTOFOROS NEOFYTIDIS
    • 2
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Section de MathématiquesUniversité de GenèveGenève 4Switzerland

Personalised recommendations