Localized exotic smoothness

Localized Exotic Smoothness

Gompf’s end-sum techniques are used to establish the existence of an infinity of non-diffeomorphic manifolds, all having the same trivial R topology, but for which the exotic differentiable structure is confined to a region which is spatially limited. Thus, the smoothness is standard outside of a region which is topologically (but not smoothly) B ×R, where B is the compact three ball. The exter...

Exotic Smoothness on Spacetime

Recent discoveries in differential topology are reviewed in light of their possible implications for spacetime models and related subjects in theoretical physics. Although not often noted, a particular smoothness (differentiability) structure must be imposed on a topological manifold before geometric or other structures of physical interest can be discussed. The recent discoveries of interest h...

Exotic Smoothness and Physics

The essential role played by differentiable structures in physics is reviewed in light of recent mathematical discoveries that topologically trivial space-time models, especially the simplest one, R , possess a rich multiplicity of such structures, no two of which are diffeomorphic to each other and thus to the standard one. This means that physics has available to it a new panoply of structure...

Exotic smoothness and spacetime models

On the Smoothness of Functors

In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.