Homological Algebra for Diffeological Vector Spaces

Enxin Wu
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引用次数: 27

Abstract

Diffeological spaces are natural generalizations of smooth manifolds, introduced by J.M.~Souriau and his mathematical group in the 1980's. Diffeological vector spaces (especially fine diffeological vector spaces) were first used by P. Iglesias-Zemmour to model some infinite dimensional spaces in~\cite{I1,I2}. K.~Costello and O.~Gwilliam developed homological algebra for differentiable diffeological vector spaces in Appendix A of their book~\cite{CG}. In this paper, we present homological algebra of general diffeological vector spaces via the projective objects with respect to all linear subductions, together with some applications in analysis.
微分向量空间的同调代数
微分空间是光滑流形的自然推广,由J.M. Souriau和他的数学小组在20世纪80年代引入。P. Iglesias-Zemmour首先用微分向量空间(特别是精细微分向量空间)在\cite{I1,I2}中建立了一些无限维空间的模型。K. Costello和O. Gwilliam在他们的著作\cite{CG}的附录A中发展了可微的微分向量空间的同调代数。本文给出了关于所有线性俯冲的经射影对象的一般微分向量空间的同调代数,并给出了在分析中的一些应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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