An inductive generalization of 1-differentiable cohomology

Abstract

In this note, we give an inductive generalization of 1-differentiable cohomology and Betti numbers of a smooth manifold endowed with a non-closed 1-form (for instance a contact manifold). Some cohomology classes in such generalized cohomology are studied and also, and an inductive generalization of coeffective 1-differentiable cohomology is considered and studied in the paper.