Questions tagged [diffeology]
The diffeology tag has no usage guidance.
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Advantages of diffeological spaces over general sheaves
I have been playing with/thinking about diffeological spaces a bit recently, and I would like understand something rather crucial before going further. First a little background:
Diffeological spaces ...
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Applications of diffeological spaces to ordinary differential geometry
Recently I've been learning more about differential geometry, and I came upon the notion of a diffeological space, which encompasses a number of already known extensions of smooth manifolds or related ...
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Diffeology as a sheaf on the site of smooth manifolds
Souriau's definition of diffeology may be phrased as defining a concrete sheaf on the category $\mathsf{Open}$ of open subsets of Euclidean/coordinate spaces. It seems to me, unless I am missing ...
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Reference for a path groupoid being a diffeological groupoid
I am looking for a reference that has a proof that a path groupoid
is a groupoid internal to the category of diffeological spaces. I do know how to prove this fact, and a proof is not hard. My reason ...
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Stacks over diffeologies
Konrad Waldorf shows in his paper one may realize a Grothendieck topology on the category of diffeological spaces. Is there any work exploring stacks over the category of diffeologies?
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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 ...
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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 ...
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(Co)limits in the category of diffeological spaces vs. category of smooth manifolds
I am wondering which (co)limits that exist in the category of smooth manifolds are preserved by the inclusion into the category of diffeological spaces? Are there any results that allow us to ...
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Is there a notion of a complex/analytic diffeological space?
I have a bit of a general question. This seems like something you can do, but I can't seem to find much reference for this.. Perhaps something like this already exists in a different guise. But, is ...
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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 ...
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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 ...
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Geometry of the irrational torus
One of the motivations of diffeology is to study singular spaces such as the irrational torus. The irrational torus $T_α$ of slope $α∈R∖Q $ as a diffeological space is given by the quotient space $ R/(...
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