We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
You are leaving Cambridge Core and will be taken to this journal's article submission site.
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.
For the group 
$G=\operatorname{PGL}_{2}$
we perform a comparison between two relative trace formulas: on the one hand, the relative trace formula of Jacquet for the quotient 
$T\backslash G/T$
, where 
$T$
is a nontrivial torus, and on the other the Kuznetsov trace formula (involving Whittaker periods), applied to nonstandard test functions. This gives a new proof of the celebrated result of Waldspurger on toric periods, and suggests a new way of comparing trace formulas, with some analogies to Langlands’ ‘Beyond Endoscopy’ program.