## Abstract

Apparently a lost theorem of Thurston [1] states that the cube of the Euler class e3 H6(BDiff Í(S1); âš) is zero where DiffÍ(S1) is the analytic orientation preserving diffeomorphisms of the circle with the discrete topology. This is in contrast with Morita's theorem [5] that the powers of the Euler class are nonzero in Hâ-(BDiff(S1); âš) where Diff(S1) is the orientation preserving C∞-diffeomorphisms of the circle with the discrete topology. The purpose of this short note is to prove that the powers of the Euler class ek Hâ-(BDiff Í(S1);) in fact are nonzero in cohomology with integer coefficients. We also give a short proof of Morita's theorem [5]. ;copy 2018 World Scientific Publishing Company.

Original language | English (US) |
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Pages (from-to) | 47-52 |

Number of pages | 6 |

Journal | Journal of Topology and Analysis |

Volume | 10 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2018 |

## Keywords

- Euler class
- analytic diffeomorphisms of the circle
- flat circle bundle
- the Haefliger space

## ASJC Scopus subject areas

- Analysis
- Geometry and Topology