## Tangent spaces of bundles and of filtered diffeological spaces

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- by J. Daniel Christensen and Enxin Wu PDF
- Proc. Amer. Math. Soc.
**145**(2017), 2255-2270 Request permission

## 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
- MR Author ID: 325401
- Email: jdc@uwo.ca
**Enxin Wu**- Affiliation: DIANA Group, Faculty of Mathematics, University of Vienna, Austria
- Email: enxin.wu@univie.ac.at
- Received by editor(s): November 1, 2015
- Published electronically: January 11, 2017
- Communicated by: Varghese Mathai
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**145**(2017), 2255-2270 - MSC (2010): Primary 57P99, 58A05
- DOI: https://doi.org/10.1090/proc/13334
- MathSciNet review: 3611335