Abstract:
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 $\mathbb{D}$. We apply holonomy pseudogroups to the investigation of $\mathbb{D}$-diffeomorphisms between quotient manifolds of the algebra $\mathbb{D}$ by lattices and between $\mathbb{D}$-smooth manifolds naturally associated with an affine manifold.
Keywords:affine manifold, manifold over the algebra of dual numbers, foliation, foliated bundle, tangent bundle, tangent manifold, torus over the algebra of dual numbers, Weil bundle.