13 citations · 14 across the 14 of their papers we have counts for
15 papers
Does the motor cortex draw on a wire plane?
Patrick Iglesias-Zemmour
The two-thirds power law of human motor control () is geometrically equivalent to constant equi-affine speed. In classical differential geometry, however, the e…
Bosonic and Fermionic Singularities in Diffeology
Patrick Iglesias-Zemmour
We explore the differential geometry of the quadrant , equipped with the subset diffeology of . We show a striking dichotomy between differential…
Geometric Quantization by Paths, Part III: The Metaplectic Anomaly
Patrick Iglesias-Zemmour
In the previous parts of this work, we established the Prequantum Groupoid as the universal geometric container for quantum mechanics. This approach, which we call t…
Geometric Quantization by Paths Part II: The General Case
Patrick Iglesias-Zemmour
In Part I, we constructed the prequantum groupoid for connected and simply connected parasymplectic spaces. This second part extends the construction to arbitrary connected parasym…
A Conformal Co-Symplectic Structure on the Space of Pseudo-Riemannian Geodesics
Patrick Iglesias-Zemmour
The classical construction of the symplectic structure on the space of geodesic trajectories via Hamiltonian reduction fails in the pseudo-Riemannian setting due to a dimensional m…
Groupoids in Diffeology
Patrick Iglesias-Zemmour
This expository paper recounts the development and application of the concept of the diffeological groupoid, from its introduction in 1985 to its use in current research. We demons…
On Diffeology of Orbit Spaces
Serap Gürer, Patrick Iglesias-Zemmour
We investigate the correspondence between the geometry of a smooth compact Lie group action on a manifold and the intrinsic smooth structure of the orbit space $\mathr…
The Geometry of Motions, Vol. I: Mechanics as Geometries
Patrick Iglesias-Zemmour
This work presents a group-theoretic interpretation of the historical evolution of mechanics, proposing that each fundamental theory of motion corresponds to a distinct geometry in…
Geometric Quantization by Paths -- Part I: The Simply Connected Case
Patrick Iglesias-Zemmour
For any connected and simply connected parasymplectic space with group of periods , we construct a prequantum groupoid $\pmb{\ma…
Why Diffeology?
Patrick Iglesias-Zemmour
Diffeology extends differential geometry to spaces beyond smooth manifolds. This paper explores diffeology's key features and illustrates its utility with examples including singul…
A Non-Trivial Principal Bundle over a Contractible Base?
Patrick Iglesias-Zemmour
We investigate the properties of a specific quotient space construction, the "warped projection'" , over a smoothly contractible base. In a previous version of this…
Diffeology and Arithmetic of Irrational Tori
Patrick Iglesias-Zemmour
The irrational torus, , originally introduced as a geometric model for quasicrystals, is a foundational object in the theory of diffeology. This paper, after recallin…
Quasifolds, Diffeology and Noncommutative Geometry
Patrick Iglesias-Zemmour, Elisa Prato
After embedding the objects quasifolds into the category {Diffeology}, we associate a C*-agebra with every atlas of any quasifold, and show how different atlases give Morita equiva…
Primary Spaces, Mackey's Obstruction, and the Generalized Barycentric Decomposition
Patrick Iglesias-Zemmour, Francois Ziegler
We call a hamiltonian N-space \emph{primary} if its moment map is onto a single coadjoint orbit. The question has long been open whether such spaces always split as (homogeneous) x…
Smooth Lie group actions are parametrized diffeological subgroups
Patrick Iglesias-Zemmour, Yael Karshon
We show that every effective smooth action of a Lie group G on a manifold M is a diffeomorphism from G onto its image in Diff(M), where the image is equipped with the subset diffeo…