After indignant with the "wonderful" solutions provided by the staff of Vodafone (read reset factory data), for those who have the problem of Home TouchWiz has stopped after updating a lollipop in S4, should disable all functions gestures as the air terminal wiew, air gestiture, etc. It can not be done from the sliding panel must be made from the settings / my device to also disable all options for each function, in addition to disable the function.
Then restart. I hope they work and the hassle of restoring factory data are avoided.