12 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…
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…
Geometric Quantization by Paths Part II: The General Case
Patrick Iglesias-Zemmour
In Part I, we established the construction of the Prequantum Groupoid for simply connected spaces. This second part extends the theory to arbitrary connected parasymplectic diffeol…
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 recalli…
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…