Harmonic morphisms and circle actions on 3- and 4-manifolds

Paul Baird

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 1, page 177-212
  • ISSN: 0373-0956

Abstract

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Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms ϕ : M → N from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on M with possible fixed points. This restricts the topology of M . In all cases, a harmonic morphism ϕ : M → N from a closed ( n + 1 ) -dimensional manifold to an n -dimensional manifold (n ≥ 2 , with M , N analytic in the case n = 2 ) determines a locally smooth circle action on M .

How to cite

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Baird, Paul. "Harmonic morphisms and circle actions on 3- and 4-manifolds." Annales de l'institut Fourier 40.1 (1990): 177-212. <http://eudml.org/doc/74870>.

@article{Baird1990,
abstract = {Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms $\phi : M\rightarrow N$ from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on $M$ with possible fixed points. This restricts the topology of $M$. In all cases, a harmonic morphism $\phi : M\rightarrow N$ from a closed $(n+1)$-dimensional manifold to an $n$-dimensional manifold (n$\ge 2$, with $M$, $N$ analytic in the case $n=2)$ determines a locally smooth circle action on $M$.},
author = {Baird, Paul},
journal = {Annales de l'institut Fourier},
keywords = {Harmonic morphisms; generalization of the analytic functions; analytic 3- manifold},
language = {eng},
number = {1},
pages = {177-212},
publisher = {Association des Annales de l'Institut Fourier},
title = {Harmonic morphisms and circle actions on 3- and 4-manifolds},
url = {http://eudml.org/doc/74870},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Baird, Paul
TI - Harmonic morphisms and circle actions on 3- and 4-manifolds
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 1
SP - 177
EP - 212
AB - Harmonic morphisms are considered as a natural generalization of the analytic functions of Riemann surface theory. It is shown that any closed analytic 3-manifold supporting a non-constant harmonic morphism into a Riemann surface must be a Seifert fibre space. Harmonic morphisms $\phi : M\rightarrow N$ from a closed 4-manifold to a 3-manifold are studied. These determine a locally smooth circle action on $M$ with possible fixed points. This restricts the topology of $M$. In all cases, a harmonic morphism $\phi : M\rightarrow N$ from a closed $(n+1)$-dimensional manifold to an $n$-dimensional manifold (n$\ge 2$, with $M$, $N$ analytic in the case $n=2)$ determines a locally smooth circle action on $M$.
LA - eng
KW - Harmonic morphisms; generalization of the analytic functions; analytic 3- manifold
UR - http://eudml.org/doc/74870
ER -

References

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