Advertisement

manuscripta mathematica

, Volume 110, Issue 3, pp 351–364 | Cite as

Topological restrictions for circle actions and harmonic morphisms

  • Radu Pantilie
  • John C. Wood

Abstract.

 Let M m be a compact oriented smooth manifold admitting a smooth circle action with isolated fixed points which are isolated as singularities as well. Then all the Pontryagin numbers of M m are zero and its Euler number is nonnegative and even. In particular, M m has signature zero. We apply this to obtain non-existence of harmonic morphisms with one-dimensional fibres from various domains, and a classification of harmonic morphisms from certain 4-manifolds.

Keywords

Smooth Manifold Euler Number Circle Action Topological Restriction Harmonic Morphism 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Radu Pantilie
    • 1
  • John C. Wood
    • 1
  1. 1.Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK. e-mail: r.pantilie@leeds.ac.uk; j.c.wood@leeds.ac.uk.GB

Personalised recommendations