Abstract
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We study a new operation named pushforward on diffeological vector pseudo-bundles,
which is left adjoint to the pullback. We show how to pushforward projective
diffeological vector pseudo-bundles to get projective diffeological vector spaces,
producing many concrete new examples, together with applications to smooth
splittings of some projective diffeological vector spaces related to geometry. This
brings new objects to diffeology from classical vector bundle theory.
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Keywords
diffeological vector pseudo-bundle, diffeological vector
space, pushforward
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Mathematical Subject Classification
Primary: 18G25
Secondary: 46S99, 57P99
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Milestones
Received: 19 January 2022
Revised: 6 December 2022
Accepted: 15 December 2022
Published: 3 May 2023
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| © 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences Publishers).
Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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