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Tangent spaces of bundles and of filtered diffeological spaces
- Source :
- Proceedings of the AMS 145(5) (2017), 2255-2270
- Publication Year :
- 2015
-
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.<br />Comment: v3: new results and improvements to exposition; 14 pages; this version to appear in Proceedings of the AMS
- Subjects :
- Mathematics - Differential Geometry
57P99, 58A05
Subjects
Details
- Database :
- arXiv
- Journal :
- Proceedings of the AMS 145(5) (2017), 2255-2270
- Publication Type :
- Report
- Accession number :
- edsarx.1510.09182
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1090/proc/13334