Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group <i>V</i>
Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group <i>V</i>
Abstract We consider generalisations of Thompson’s group V , denoted by <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>V</m:mi> <m:mi>r</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>Σ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> ${V_{r}(\Sigma)}$ , which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>V</m:mi> …