Long exact sequences for de Rham cohomology of diffeological spaces

TL;DR

This paper introduces de Rham cohomology with compact support for diffeological spaces and establishes the existence of three long exact sequences, including for subcartesian spaces, advancing the understanding of their cohomological properties.

Contribution

It develops the concept of de Rham cohomology with compact support for diffeological spaces and proves the existence of long exact sequences in this context.

Findings

Long exact sequences exist for de Rham cohomology of diffeological subcartesian spaces.

The paper extends cohomological tools to a broader class of diffeological spaces.

It provides a framework for analyzing cohomology with compact support in diffeology.

Abstract

In this paper we present the notion of de Rham cohomology with compact support for diffeological spaces. Moreover we shall discuss the existence of three long exact sequences. As a concrete example, we show that long exact sequences exist for the de Rham cohomology of diffeological subcartesian spaces.