Why diffeology?
March 1, 2025
 
Why bother with diffeology? Classical differential geometry works well enough, doesn’t it? Theanswer, to put it bluntly, is no. From the awkwardness of handling singularities to the limitationsimposed by infinite-dimensional spaces, the traditional framework is riddled with inadequacies. Diffeology offers not just a patch, but a fundamental overhaul, a comprehensive theory, providinga more natural and powerful foundation for smoothness. This paper will convince you that it’s atheory worth learning.
Submitted for publication.http://math.huji.ac.il/~piz/documents/WD.pdfshapeimage_3_link_0