Abstract: The classical setting of property (T) applies to topological (usually locally compact) groups. It says that all *continuous* representations of the group have a spectral gap. Clearly, this seems to depend on the topology of the group. We showed that, like in the geometric case, property (T) does not in fact depend on the topology of the group, but it depends only on the large-scale structure. This shows that topological groups are not in fact the most natural setting to study property (T). Instead we can work in the category of so-called *bornological groups*, which are groups with a large-scale geometric structure. This talk is based on joint work in progress with Romain Tessera.