The "center" theory of this mathematical object is used to reduce the dimension of a dynamical system around equilibrium points.  
The "center" theory of this mathematical object is used to reduce the dimension of a dynamical system around equilibrium points.  Nash's Embedding Theorem provides the conditions for two algebraic ones to be equivalent.  "Surgery" must be done when attaching a "handle" to one of these mathematical objects, which surgery theory can alter if they are over dimension five. Infinitely differentiable ones are called smooth. Every smooth kind of this object under four dimensions is topological.  Riemannian ones contain a metric tensor and are acted on by Ricci flow, a method used to prove the PoincarÃ© Conjecture, which deals with three-dimensional ones.  For 10 points, name this mathematical object, consisting of a topological space that is locally Euclidean, a generalization of a surface.
The "center" theory of this mathematical object is used to reduce the dimension of a dynamical system around equilibrium points.  
manifold