## Mickey Mouse Sphere Theorem

The Mickey mouse theorem assures that a connected positive curvature graph of positive dimension is a sphere.

For a one-dimensional simplicial complex, the sign less Hodge operator can be written as L-g, where g is the inverse of L. This leads to a Laplace equation shows solutions are given by a two-sided random walk.

The strong ring is a category of geometric objects G which are disjoint unions of products of

simplicial complexes. Each has a Dirac operator D and a connection operator L. Both are related in

various ways to topology.