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Questions tagged [diffeology]

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Inducing a model structure using a cosimplicial object

In a recent paper, Hiroshi Kihara induced a model structure on the category of diffeological spaces. He generates the classes of fibrations, cofibrations, and weak equivalences by constructing a ...
3
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0answers
95 views

Construction of differential of a smooth map between diffeological spaces with respect to internal tangent spaces

According to page 5 , definition 3.1 of https://arxiv.org/pdf/1411.5425.pdf, there is a notion of Internal Tangent Space of a Diffeological space $X$ at a point $x \in X$. Basically if $x \in X$, they ...
4
votes
0answers
88 views

When is the quotient of a manifold by a discrete group of diffeomorphisms a diffeological covering space?

I was reading An Introduction to Diffeology by Patrick Iglesias-Zemmour and he defines a diffeological covering space as a diffeological fiber bundle with discrete fiber. My question: Consider a ...
7
votes
1answer
337 views

Differential forms on standard simplices via Whitney extension vs diffeological structure

The standard simplices $\Delta^n \subset \{\mathbf{x}\in\mathbb{R}^{n+1}\mid x_0 + \ldots + x_n =1 \} =: \mathbb{A}^n$ carry two natural sorts of smooth differential forms: Those differential forms ...