Skip to main content
SpringerLink
Log in

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

  • Published:
Transformation Groups Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Borel, J.-P. Serre, Groupes de Lie et puissances réduites de Steenrod, Amer. J. Math. 75 (1953), 409–448.

    Article  MathSciNet  Google Scholar 

  2. H. Duan, S. Wang, Non-zero degree maps between 2n-manifolds, Acta Math. Sin. (Engl. Ser.) 20 (2004), 1–14.

    Article  MathSciNet  Google Scholar 

  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. C. Kennedy, Construction of maps by Postnikov towers, PhD Thesis, Ohio State University (2018).

  5. M. Mimura, H. Toda, Homotopy groups of SU(3), SU(4) and Sp(2), J. Math. Kyoto Univ. 3 (1964), 217–250.

    Article  MathSciNet  Google Scholar 

  6. C. Neofytidis, Degrees of self-maps of products, Int. Math. Res. Not. IMRN 22 (2017), 6977–6989.

    MathSciNet  MATH  Google Scholar 

  7. T. Püttmann, Cohomogeneity one manifolds and selfmaps of nontrivial degree, Transform. Groups 14 (2009), 225–247.

    Article  MathSciNet  Google Scholar 

  8. T. Püttmann, A. Rigas, Presentations of the first homotopy groups of the unitary groups, Comment. Math. Helv. 78 (2003), 648–662.

    Article  MathSciNet  Google Scholar 

  9. H. Sun, S. Wang, J. Wu, H. Zheng, Self-mapping degrees of 3-manifolds, Osaka J. Math. 49 (2012), 247–269.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA

    JEAN-FRANÇOIS LAFONT

  2. Section de Mathématiques, Université de Genève, 2-4 rue du Lièvre, Case postale 64, 1211, Genève 4, Switzerland

    CHRISTOFOROS NEOFYTIDIS

Authors
  1. JEAN-FRANÇOIS LAFONT
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. CHRISTOFOROS NEOFYTIDIS
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to JEAN-FRANÇOIS LAFONT.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

LAFONT, JF., NEOFYTIDIS, C. SETS OF DEGREES OF MAPS BETWEEN SU(2)-BUNDLES OVER THE 5-SPHERE. Transformation Groups 24, 1147–1155 (2019). https://doi.org/10.1007/s00031-018-9490-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00031-018-9490-9

Search

Navigation