Finiteness Obstructions of Equivariant Fibrations

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Abstract

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.

Original languageEnglish
Pages (from-to)627-637
Number of pages11
JournalPublications of the Research Institute for Mathematical Sciences
Volume27
Issue number4
DOIs
Publication statusPublished - Jan 1 1991

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CW-complex
Fibration
Finiteness
Obstruction
Equivariant
Homotopy
Compact Lie Group
Euler Characteristic
Homomorphism
Functor
Abelian group
Subgroup
Closed

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Finiteness Obstructions of Equivariant Fibrations. / Sumi, Toshio.

In: Publications of the Research Institute for Mathematical Sciences, Vol. 27, No. 4, 01.01.1991, p. 627-637.

Research output: Contribution to journalArticle

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