Function spaces on formal manifolds

Abstract

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the foundational framework of formal manifolds. In this paper, we study various function spaces on formal manifolds, including generalizations of vector-valued generalized functions and vector-valued distributions on smooth manifolds to the setting of formal manifolds.