Set the current path as a class on ember's application view.

application.js

    App.ApplicationView = Ember.View.extend({
      classNames: ['app'], // Static classes here.
      classNameBindings: ['classForPath'], // Your dynamic path here.
      classForPath: (function() {
        var currentPath = this.get('controller.currentPath') || '';
        currentPath = Ember.String.decamelize(currentPath);
        currentPath = currentPath.split('.').join('-');
        return currentPath;
      }).property('controller.currentPath')
    });