Topological restrictions for circle actions and harmonic morphisms
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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.
KeywordsSmooth Manifold Euler Number Circle Action Topological Restriction Harmonic Morphism
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