Long exact sequences for de Rham cohomology of diffeological spaces
  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. 
Tadayuki Haraguchi
math.AT