According to specification android specification:
To enable the icon for up navigation (which displays the "up" indicator next to the icon), call setDisplayHomeAsUpEnabled(true) on your ActionBar:
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.main);
ActionBar actionBar = getActionBar();
actionBar.setDisplayHomeAsUpEnabled(true);
...
}
So you should set actionBar.setDisplayHomeAsUpEnabled(false);
UPDATE:
I test next code with ActionBar sherlock and it's work. There is no back arrow:
getSupportActionBar().setIcon(R.drawable.ic_launcher);
getSupportActionBar().setDisplayShowTitleEnabled(true);
getSupportActionBar().setTitle(R.string.about_event_location);
getSupportActionBar().setDisplayHomeAsUpEnabled(false);