Formal manifolds: local structure of morphisms, and formal submanifolds

TL;DR

This paper advances the theory of formal manifolds by analyzing the local structure of morphisms and formal submanifolds, building on previous work on their foundational aspects and function spaces.

Contribution

It introduces new results on the local structure of constant rank morphisms and formal submanifolds within the framework of formal manifolds.

Findings

Analysis of the local structure of constant rank morphisms

Development of the theory of formal submanifolds

Extension of foundational framework for 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 three previous papers, we introduce the notion of formal manifolds and study their basic theory, focusing on function spaces and Poincare's lemma. In this paper, we further explore the foundational framework of formal manifolds, including the local structure of constant rank morphisms (such as inverse function theorem and constant rank theorems) as well as the theory of formal submanifolds.