22 citations · 77 across the 17 of their papers we have counts for
20 papers
Smooth maps on convex sets
Yael Karshon, Jordan Watts
There are several notions of a smooth map from a convex set to a cartesian space. Some of these notions coincide, but not all of them do. We construct a real-valued function on a c…
Bicategories of Action Groupoids
Carla Farsi, Laura Scull, Jordan Watts
We prove that the 2-category of action Lie groupoids localised in the following three different ways yield equivalent bicategories: localising at equivariant weak equivalences à la…
The Bicategory of Lie Groupoids within Diffeological Groupoids
Jordan Watts
We consider the localisation of the 2-category of diffeological groupoids at weak equivalences from the perspective of anafunctors, and with this language, prove that the localisat…
Diffeological submanifolds and their friends
Yael Karshon, David Miyamoto, Jordan Watts
A smooth manifold hosts different types of submanifolds, including embedded, weakly-embedded, and immersed submanifolds. The notion of an immersed submanifold requires additional s…
Sheaves, principal bundles, and Čech cohomology for diffeological spaces
Derek Krepski, Jordan Watts, Seth Wolbert
The purpose of this note is to define sheaves for diffeological spaces and give a construction of their Čech cohomology. As an application, we prove that the first degree Čech coho…
Classifying spaces and Bredon (co)homology for transitive groupoids
Carla Farsi, Laura Scull, Jordan Watts
We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomol…
Diffeological, Frölicher, and Differential Spaces
Augustin Batubenge, Yael Karshon, Jordan Watts
Differential calculus on Euclidean spaces has many generalisations. In particular, on a set , a diffeological structure is given by maps from open subsets of Euclidean spaces to…
Differential Cocycles and Dixmier-Douady Bundles
Derek Krepski, Jordan Watts
This paper exhibits equivalences of 2-stacks between certain models of -gerbes and differential 3-cocycles. We focus primarily on the model of Dixmier-Douady bundles,…
Orbit Spaces of Linear Circle Actions
Suzanne Craig, Naiche Downey, Lucas Goad +2
In this paper, it is shown that non-isomorphic effective linear circle actions yield non-diffeomorphic differential structures on the corresponding orbit spaces.
Symplectic quotients and representability: the circle action case
Jordan Watts
Let act on a symplectic manifold in a Hamiltonian fashion with momentum map . Fix a value of . There is a question of whether the symplectic quotient at is diff…
The diffeology of Milnor's classifying space
Jean-Pierre Magnot, Jordan Watts
We define a diffeology on the Milnor classifying space of a diffeological group , constructed in a similar fashion to the topological version using an infinite join. Besides obt…
Tame Circle Actions
Susan Tolman, Jordan Watts
In this paper, we consider Sjamaar's holomorphic slice theorem, the birational equivalence theorem of Guillemin and Sternberg, and a number of important standard constructions that…
The Differential Structure of an Orbifold
Jordan Watts
We prove that the underlying set of an orbifold equipped with the ring of smooth real-valued functions completely determines the orbifold atlas. Consequently, we obtain an essentia…
Basic Forms and Orbit Spaces: a Diffeological Approach
Yael Karshon, Jordan Watts
If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic d…
Diffeological Coarse Moduli Spaces of Stacks over Manifolds
Jordan Watts, Seth Wolbert
In this paper, we consider diffeological spaces as stacks over the site of smooth manifolds, as well as the "underlying" diffeological space of any stack. More precisely, we consid…
The Orbit Space and Basic Forms of a Proper Lie Groupoid
Jordan Watts
A classical result in differential geometry states that for a free and proper Lie group action, the quotient map to the orbit space induces an isomorphism between the de Rham compl…
Diffeologies, Differential Spaces, and Symplectic Geometry
Jordan Watts
Diffeological and differential spaces are generalisations of smooth structures on manifolds. We show that the "intersection" of these two categories is isomorphic to Frölicher spac…
Differential Spaces, Vector Fields, and Orbit-Type Stratifications
Jordan Watts
Let be a Lie group, and let be a symplectic manifold. If admits a Hamiltonian action on with momentum map , then , the zero-level set of , the orbi…
The orientation-preserving diffeomorphism group of S^2 deforms to SO(3) smoothly
Jiayong Li, Jordan Alan Watts
Smale proved that the orientation-preserving diffeomorphism group of S^2 has a continuous strong deformation retraction to SO(3). In this paper, we construct such a strong deformat…
Regular Points of a Subcartesian Space
Tsasa Lusala, Jȩdrzej Śniatycki, Jordan Watts
We discuss properties of the regular part of a subcartesian space . We show that is open and dense in and the restriction to of the tangent bun…