DISMANTLABLE CLASSIFYING SPACE FOR THE FAMILY OF PARABOLIC SUBGROUPS OF A RELATIVELY HYPERBOLIC GROUP
2017 ◽
Vol 18
(2)
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pp. 329-345
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Keyword(s):
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.
2008 ◽
Vol 18
(01)
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pp. 97-110
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2005 ◽
Vol 15
(05n06)
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pp. 893-906
2015 ◽
Vol 25
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pp. 689-723
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2018 ◽
Vol 167
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pp. 2189-2241
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Vol 157
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pp. 297-319
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Vol 25
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pp. 81-111
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Vol 07
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pp. 345-359
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Vol 22
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pp. 1250016
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