Algebras of Smooth Functions and Holography of Traversing Flows

Abstract

Let be a smooth compact manifold and a vector field on which admits a smooth function such that 0 Let be the boundary of We denote by the algebra of smooth functions on and by the algebra of smooth functions on With the help of we introduce two subalgebras and of and prove under mild hypotheses that the topological tensor product Thus the topological algebras and viewed as allow for a reconstruction of As a result and allow for the recovery of the smooth topological type of the bulk