Function spaces on formal manifolds

TL;DR

This paper explores the structure of function spaces on formal manifolds, extending classical concepts like distributions to this new setting, and builds on previous foundational work in formal manifolds and Lie groups.

Contribution

It introduces and analyzes various function spaces on formal manifolds, generalizing classical distribution theory to this novel geometric context.

Findings

Development of generalized vector-valued functions on formal manifolds

Extension of distribution theory to formal manifolds

Foundational framework for 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.