Mayer–vietoris sequence for differentiable/diffeological spaces

Norio Iwase, Nobuyuki Izumida

研究成果: 著書/レポートタイプへの貢献

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.

元の言語英語
ホスト出版物のタイトルTrends in Mathematics
出版者Springer International Publishing
ページ123-151
ページ数29
DOI
出版物ステータス出版済み - 1 1 2019

出版物シリーズ

名前Trends in Mathematics
ISSN(印刷物)2297-0215
ISSN(電子版)2297-024X

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Differentiable
Partition of Unity
CW-complex
Exact Sequence
Theorem
De Rham Cohomology
Loop Space
Differential Forms
Curvilinear integral
Topological space
Cohomology

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Iwase, N., & Izumida, N. (2019). Mayer–vietoris sequence for differentiable/diffeological spaces. : Trends in Mathematics (pp. 123-151). (Trends in Mathematics). Springer International Publishing. https://doi.org/10.1007/978-981-13-5742-8_8

Mayer–vietoris sequence for differentiable/diffeological spaces. / Iwase, Norio; Izumida, Nobuyuki.

Trends in Mathematics. Springer International Publishing, 2019. p. 123-151 (Trends in Mathematics).

研究成果: 著書/レポートタイプへの貢献

Iwase, N & Izumida, N 2019, Mayer–vietoris sequence for differentiable/diffeological spaces. : Trends in Mathematics. Trends in Mathematics, Springer International Publishing, pp. 123-151. https://doi.org/10.1007/978-981-13-5742-8_8
Iwase N, Izumida N. Mayer–vietoris sequence for differentiable/diffeological spaces. : Trends in Mathematics. Springer International Publishing. 2019. p. 123-151. (Trends in Mathematics). https://doi.org/10.1007/978-981-13-5742-8_8
Iwase, Norio ; Izumida, Nobuyuki. / Mayer–vietoris sequence for differentiable/diffeological spaces. Trends in Mathematics. Springer International Publishing, 2019. pp. 123-151 (Trends in Mathematics).
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