Differential forms on diffeological spaces and diffeological gluing, I

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-04-07 DOI:10.1016/j.topol.2025.109387

Ekaterina Pervova

引用次数: 0

Abstract

This paper aims to describe the behavior of diffeological differential forms under the operation of gluing of diffeological spaces along a smooth map. In the diffeological context, two ways of looking at diffeological forms are available, that of the vector space

Ω^{m} (X)

of all m-forms, and that of the pseudo-bundle

Λ^{m} (X)

of values of these forms. We describe the behavior of the former under a gluing of diffeological spaces.

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微分形式的微分空间和微分胶合，1

本文旨在描述微分空间沿光滑映射胶合作用下微分形式的行为。在衍射上下文中，有两种观察衍射形式的方法，一种是所有m形式的向量空间Ωm(X)，另一种是这些形式的值的伪束Λm(X)。我们描述了前者在微分空间胶合下的行为。

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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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.