To register an application event, the notifier (or the publisher component) should have the following snippet in the markup:

<aura:registerEvent name="appEvent" type="c:appEvent"/>

Notice that we need the name attribute here, but it is not used anywhere else. Also, notice that for the type of the event, we specify the event filename, prefixed with a colon :, and the namespace (for an application with no namespace, we always use c:).