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Topological restrictions for circle actions and harmonic morphisms

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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.

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Authors and Affiliations

  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

    Radu Pantilie & John C. Wood

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  1. Radu Pantilie
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  2. John C. Wood
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Received: 16 May 2002 Published online: 14 February 2003

Mathematics Subject Classification (2000): 58E20, 53C43, 57R20.

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Pantilie, R., Wood, J. Topological restrictions for circle actions and harmonic morphisms. manuscripta math. 110, 351–364 (2003). https://doi.org/10.1007/s00229-002-0342-4

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  • DOI: https://doi.org/10.1007/s00229-002-0342-4

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