Mayer–vietoris sequence for differentiable/diffeological spaces

Norio Iwase, Nobuyuki Izumida

研究成果: Chapter in Book/Report/Conference proceedingChapter

1 被引用数 (Scopus)


The idea of a space with smooth structure is a generalization of an idea of a manifold. K. T. Chen introduced such a space as a differentiable space in his study of a loop space to employ the idea of iterated path integrals [2–5]. Following the pattern established by Chen, Souriau [10] introduced his version of a space with smooth structure, which is called a diffeological space. These notions are strong enough to include all the topological spaces. However, if one tries to show de Rham theorem, he must encounter a difficulty to obtain a partition of unity and thus the Mayer–Vietoris exact sequence in general. In this paper, we introduce a new version of differential forms to obtain a partition of unity, the Mayer–Vietoris exact sequence, and a version of de Rham theorem in general. In addition, if we restrict ourselves to consider only CW complexes, we obtain de Rham theorem for a genuine de Rham complex, and hence the genuine de Rham cohomology coincides with the ordinary cohomology for a CW complex.

ホスト出版物のタイトルTrends in Mathematics
出版社Springer International Publishing
出版ステータス出版済み - 2019


名前Trends in Mathematics

All Science Journal Classification (ASJC) codes

  • 数学 (全般)


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