An Eilenberg–Ganea phenomenon for actions with virtually cyclic stabilisers | Zendy

Martin Fluch | Zendy; Ian J. Leary | Zendy

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An Eilenberg–Ganea phenomenon for actions with virtually cyclic stabilisers

Author(s) -

Martin Fluch,

Ian J. Leary

Publication year - 2014

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/219

Subject(s) - mathematics , coxeter group , dimension (graph theory) , classifying space , cohomology , pure mathematics , algebraic number , cohomological dimension , space (punctuation) , group (periodic table) , phenomenon , algebra over a field , combinatorics , mathematical analysis , computer science , physics , quantum mechanics , operating system , chemistry , organic chemistry

In dimension 3 and above, Bredon cohomology gives an acurate purely algebraic description of the minimal dimension of the classifying space for actions of a group with stabilisers in any given family of subgroups. For some Coxeter groups and the family of virtually cyclic subgroups we show that the Bredon cohomological dimension is 2 while the Bredon geometric dimension is 3.

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