Geodesic
Bredon cohomological finiteness conditions for generalisations of Thompson groups
Conchita Martínez-Pérez1 ; Brita E. A. Nucinkis2
1Universidad de Zaragoza, Spain
2Royal Holloway University of London, Egham, UK
Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 931-959

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DOI

We define a family of groups that generalises Thompson’s groups T and G, and also those of Higman, Stein and Brin. For groups in this family we describe centralisers of finite subgroups and show that for a given finite subgroup Q there are finitely many conjugacy classes of finite subgroups isomorphic to Q. We consider groups of type quasi-F​∞​. This is a property slightly weaker than possessing a finite type model for the classifying space for proper actions E​G. We give criteria for the T versions of our groups to be of type quasi-F​∞​. We also generalise some well-known properties of ordinary cohomology to Bredon cohomology.
DOI : 10.4171/ggd/211
Classification : 20-XX
Mots-clés : Bredon cohomology, Thompson groups, finiteness properties

Conchita Martínez-Pérez  1   ; Brita E. A. Nucinkis  2

1 Universidad de Zaragoza, Spain
2 Royal Holloway University of London, Egham, UK 
Conchita Martínez-Pérez; Brita E. A. Nucinkis. Bredon cohomological finiteness conditions for generalisations of Thompson groups. Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 931-959. doi: 10.4171/ggd/211
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     title = {Bredon cohomological finiteness conditions for generalisations of {Thompson} groups},
     journal = {Groups, geometry, and dynamics},
     pages = {931--959},
     year = {2013},
     volume = {7},
     number = {4},
     doi = {10.4171/ggd/211},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/211/}
}
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