They way to do this:

// get parent category slug
$parentCatList = get_category_parents($cat,false,',');
$parentCatListArray = split(",",$parentCatList);
$topParentName = $parentCatListArray[0];
$sdacReplace = array(" " => "-", "(" => "", ")" => "");
$topParent = strtolower(strtr($topParentName,$sdacReplace));

To test this you can simply put it in your header and echo out $topParent and you will see the “slug” of the category.
If you want to see the category name and not necessarily the slug – you can simply echo $topParentName.