People said "android:parentActivityName will give you a back button on your action bar":
However that is not true:
This line of the code will give you the back button:
getSupportActionBar().setDisplayOptions(getSupportActionBar().getDisplayOptions() | ActionBar.DISPLAY_HOME_AS_UP);
|int||DISPLAY_HOME_AS_UP||Display the 'home' element such that it appears as an 'up' affordance.|
This will give your the back button , but doesn't give you the functionality of show you the previous page. The redirecting should be done in another place.
In AndroidManifest.xml, by puting this in an activity:
It is doesn't matter the value, but you must have it.