arXiv 1602.048632016-02math.GRmath.GT

Dismantlable classifying space for the family of parabolic subgroups of a relatively hyperbolic group

Eduardo Martinez-Pedroza, Piotr Przytycki

备注：: Version accepted for publication in J. Inst. Math. Jussieu
DOI：: 10.1017/S147474801700010X

英文摘要：

Let $G$ be a group hyperbolic relative to a finite collection of subgroups $\mathcal P$. Let $\mathcal F$ be the family of subgroups consisting of all the conjugates of subgroups in $\mathcal P$, all their subgroups, and all finite subgroups. Then there is a cocompact model for $E_{\mathcal F} G$. This result was known in the torsion-free case. In the presence of torsion, a new approach was necessary. Our method is to exploit the notion of dismantlability. A number of sample applications are discussed.

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