URegina Topology & Geometry Seminar: Martin Frankland

So far, we learned that a deformation problem is controlled by a DG Lie algebra, and that solutions to the deformation problem correspond to Maurer-Cartan (MC) elements. However, different MC elements may yield equivalent deformations! The DG Lie algebra gives rise to a group called the gauge group, which acts on the space of MC elements. Two MC elements yield equivalent deformations if and only if they are related by the gauge action. We will illustrate this machinery in the case of deformations of algebras.