Equivariant Heegaard genus of reducible 3-manifolds

Abstract The equivariant Heegaard genus of a 3-manifold W with the action finite group G diffeomorphisms is smallest an splitting for . Although reducible manifold and although if reducible, there essential sphere, we show that may be super-additive, additive, or sub-additive under connected sum. Using thin position theory 3-dimensional orbifolds, establish sharp bounds on manifolds, similar to those known tunnel number. Along way, make use new invariant which much better behaved sums.