Derivatives, Products, and Pullbacks in Forman's Combinatorial Differential Forms

Abstract

We study derivatives, closedness, and exactness of 0-forms and 1-forms in the theory of combinatorial differential forms constructed by Robin Forman. We give an example of a closed but not exact 1-form on a non-simply connected domain. We give a sufficient condition on the domain for a closed 1-form to be exact. We show that the product of forms proposed by Forman is not anti-commutative. We propose a definition of pullbacks of forms and show that this operation has several properties analogous to pullbacks on smooth forms.