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# A note on circle actions on 5- and 6-dimensional manifolds

Type of Publication: | Preprint |

URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-20206 |

Author: | Huck, Wolfgang |

Year of publication: | 1997 |

Series: | Konstanzer Schriften in Mathematik und Informatik ; 27 |

Summary: |
M. Aubry and J.-M. Lemaire proved in 1985 that a simply connected 5-manifold M admits a free circle action if and only if H*(M) is free or, what amounts to the same, if and only if M is a connected sum of S3-bundles over S2. We show that H*(M) being free is as well equivalent to the existence of a semifree action (or, even better: to the existence of an action with only fixed points, free and isolated exceptional orbits) on M.
Moreover, we use results on Brieskorn manifolds due to J. Milnor to prove that every irreducible (i.e not splittable into a non-trivial connected sum) simply connected spin-5-manifold can be endowed with a fixed point free circle action. Finally we show that a differentiable, simply connected 6-manifold with free cohomology admits a free S1-action if and only if it admits an action without fixed points. |

Subject (DDC): | 004 Computer Science |

Link to License: | Terms of use |

Checksum:
MD5:c50dbdb1c9810f7bfe9967afb5efb865

HUCK, Wolfgang, 1997. A note on circle actions on 5- and 6-dimensional manifolds

@unpublished{Huck1997circl-6188, title={A note on circle actions on 5- and 6-dimensional manifolds}, year={1997}, author={Huck, Wolfgang} }

preprint_027.pdf | 90 |