20250314 Differentiable Stacks IV

Two weeks ago, we were introduced to the notion of a stack on the category of manifolds. However, not all these stacks lend themselves well to doing geometry. In this talk, we will focus on class of stacks for which one can do geometry, namely the differentiable stacks. These are stacks, which can be covered by smooth manifolds in a consistent manner. After understanding all the definitions, we will discuss examples and non-examples of differentiable stacks. In addition, we will begin with relating the geometry of the covers to the geometry of the underlying stacks.