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Tangent spaces of bundles and of filtered diffeological spaces

Authors: J. Daniel Christensen and Enxin Wu
Journal: Proc. Amer. Math. Soc. 145 (2017), 2255-2270
MSC (2010): Primary 57P99, 58A05
Published electronically: January 11, 2017
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Abstract: We show that a diffeological bundle gives rise to an exact sequence of internal tangent spaces. We then introduce two new classes of diffeological spaces, which we call weakly filtered and filtered diffeological spaces, whose tangent spaces are easier to understand. These are the diffeological spaces whose categories of pointed plots are (weakly) filtered. We extend the exact sequence one step further in the case of a diffeological bundle with filtered total space and base space. We also show that the tangent bundle $ T^H X$ defined by Hector is a diffeological vector space over $ X$ when $ X$ is filtered or when $ X$ is a homogeneous space, and therefore agrees with the dvs tangent bundle introduced by the authors in a previous paper.

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Additional Information

J. Daniel Christensen
Affiliation: Department of Mathematics, Western University, London, Ontario, Canada

Enxin Wu
Affiliation: DIANA Group, Faculty of Mathematics, University of Vienna, Austria

Keywords: Tangent space, tangent bundle, diffeological bundle
Received by editor(s): November 1, 2015
Published electronically: January 11, 2017
Communicated by: Varghese Mathai
Article copyright: © Copyright 2017 American Mathematical Society

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