Abstract:
© 2019, Allerton Press, Inc. We study properties of the holonomy pseudogroup on a total immersed transversal of the canonical foliation on a smooth manifold over the algebra of dual numbers ⅅ. We apply holonomy pseudogroups to the investigation of ⅅ-diffeomorphisms between quotient manifolds of the algebra ⅅ by lattices and between ⅅ-smooth manifolds naturally associated with an affine manifold.