A note on the orderability of Dehn fillings of the manifold v2503

We show that Dehn filling on the manifold [Formula: see text] results in a non-orderable space for all rational slopes in the interval [Formula: see text]. This is consistent with the L-space conjecture, which predicts that all fillings will result in a non-orderable space for this manifold.

Farrell–Jones via Dehn fillings

Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the pre-images of infinite order subgroups have a certain structure of a free product. We then apply this result to establish the Farrell–Jones conjecture for groups hyperbolic relative to a family of residually finite subgroups satisfying the Farrell–Jones conjecture, partially recovering a result of Bartels.