Constructing and forbidding automorphisms in lifted maps

We use an algebraic description of surfaces with boundary to study covering maps. The focus is on the relationship between automorphisms in the base and lifted maps. We show how to introduce and/or prohibit additional au­ tomorphisms in the lift. Using this control we give proofs of MacBeath's Theorem, Griinbaum's Conjecture, and settle a conjecture of N ede 1 a and Skoviera.