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Exterior bundles in diffeology

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Abstract

We explore several notions of k-form at a point in a diffeological space, construct bundles of such k-forms, and compare sections of these bundles to differential forms. As they are defined locally, our k-forms can contain more information than the values of differential forms contain, and we illustrate this with many examples. To organize our work, we develop the basic theory of diffeological vector pseudo-bundles, including a detailed understanding of their limits and colimits, as well as a variety of fibrewise operations such as products, direct sums, tensor products, exterior powers and dual bundles.

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Authors and Affiliations

  1. Department of Mathematics, University of Western Ontario, London, N6A 5B7, ON, Canada

    J. Daniel Christensen

  2. Shantou University, Guangdong, 515063, P.R. China

    Enxin Wu

Authors
  1. J. Daniel Christensen
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  2. Enxin Wu
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Corresponding author

Correspondence to Enxin Wu.

Additional information

The second author was partially supported by NNSF of China (No. 11971141 and 112530).

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Christensen, J.D., Wu, E. Exterior bundles in diffeology. Isr. J. Math. 253, 673–713 (2023). https://doi.org/10.1007/s11856-022-2372-9

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  • DOI: https://doi.org/10.1007/s11856-022-2372-9

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