Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Pseudo-bundles of exterior algebras as diffeological Clifford modules (1604.04861v2)

Published 17 Apr 2016 in math.DG

Abstract: We consider the diffeological pseudo-bundles of exterior algebras, and the Clifford action of the corresponding Clifford algebras, associated to a given finite-dimensional and locally trivial diffeological vector pseudo-bundle, as well as the behavior of the former three constructions (exterior algebra, Clifford action, Clifford algebra) under the diffeological gluing of pseudo-bundles. Despite these being our main object of interest, we dedicate significant attention to the issues of compatibility of pseudo-metrics, and the gluing-dual commutativity condition, that is, the condition ensuring that the dual of the result of gluing together two pseudo-bundles can equivalently be obtained by gluing together their duals (this is not automatic in the diffeological context). We show that, assuming that the dual of the gluing map, which itself does not have to be a diffeomorphism, on the total space is one, the commutativity condition is satisfied, via a very natural map, which in addition turns out to be an isometry for the natural pseudo-metrics on the pseudo-bundles involved.

Summary

We haven't generated a summary for this paper yet.