Frolicher structures, diffieties, and a formal KP hierarchy

TL;DR

This paper introduces a new framework for diffieties using Frolicher structures, leading to a natural Vinogradov sequence and a well-posed KP hierarchy under certain conditions.

Contribution

It provides a novel definition of diffieties via Frolicher structures and constructs a well-posed KP hierarchy assuming the existence of a suitable derivation.

Findings

Established a Frolicher-structure-based definition of diffieties.

Derived a natural Vinogradov sequence from this framework.

Constructed a well-posed KP hierarchy under specific assumptions.

Abstract

We propose a definition of a diffiety based on the theory of Frolicher structures. As a consequence, we obtain a natural Vinogradov sequence and, under the assumption of the existence of a suitable derivation, we can form on it a Kadomtsev-Petviashvili hierarchy which is well-posed.