### Abstract

Let G be a compact Lie group and E?B a G-fibration. We define a homomorphism Wa^{G}(B)?U^{G}(B) into Wa^{G}(E)?U^{G}(E) sending the pair of the finiteness obstruction of B and the equivariant Euler characteristic of B to that of E. Here Wa^{G} is the functor from the G-homotopy category of finitely dominated G-CW complexes into the category of abelian groups given by W. Lück. By making use of this, we show that if H and K are closed subgroups with H or K normal such that W(HK) is not finite, G _{H}X is K-homotopy equivalent to a finite K-CW complex.

Original language | English |
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Pages (from-to) | 627-637 |

Number of pages | 11 |

Journal | Publications of the Research Institute for Mathematical Sciences |

Volume | 27 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1991 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

**Finiteness Obstructions of Equivariant Fibrations.** / Sumi, Toshio.

Research output: Contribution to journal › Article

*Publications of the Research Institute for Mathematical Sciences*, vol. 27, no. 4, pp. 627-637. https://doi.org/10.2977/prims/1195169422

}

TY - JOUR

T1 - Finiteness Obstructions of Equivariant Fibrations

AU - Sumi, Toshio

PY - 1991/1/1

Y1 - 1991/1/1

N2 - Let G be a compact Lie group and E?B a G-fibration. We define a homomorphism WaG(B)?UG(B) into WaG(E)?UG(E) sending the pair of the finiteness obstruction of B and the equivariant Euler characteristic of B to that of E. Here WaG is the functor from the G-homotopy category of finitely dominated G-CW complexes into the category of abelian groups given by W. Lück. By making use of this, we show that if H and K are closed subgroups with H or K normal such that W(HK) is not finite, G HX is K-homotopy equivalent to a finite K-CW complex.

AB - Let G be a compact Lie group and E?B a G-fibration. We define a homomorphism WaG(B)?UG(B) into WaG(E)?UG(E) sending the pair of the finiteness obstruction of B and the equivariant Euler characteristic of B to that of E. Here WaG is the functor from the G-homotopy category of finitely dominated G-CW complexes into the category of abelian groups given by W. Lück. By making use of this, we show that if H and K are closed subgroups with H or K normal such that W(HK) is not finite, G HX is K-homotopy equivalent to a finite K-CW complex.

UR - http://www.scopus.com/inward/record.url?scp=85007955467&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007955467&partnerID=8YFLogxK

U2 - 10.2977/prims/1195169422

DO - 10.2977/prims/1195169422

M3 - Article

AN - SCOPUS:85007955467

VL - 27

SP - 627

EP - 637

JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

SN - 0034-5318

IS - 4

ER -