# Mayer–vietoris sequence for differentiable/diffeological spaces

1 被引用数 (Scopus)

## 抄録

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.

本文言語 英語 Trends in Mathematics Springer International Publishing 123-151 29 https://doi.org/10.1007/978-981-13-5742-8_8 出版済み - 2019

### 出版物シリーズ

名前 Trends in Mathematics 2297-0215 2297-024X

• 数学 (全般)

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