Algebras of Smooth Functions and Holography of Traversing Flows
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 .
