Preface

At the Beginning

Diffeology, the Axiomatic

The Irrational Tori 8

Generating Families, Dimension

Cartan-De-Rham Calculus

Diffeology Fiber Bundles

Homotopy Theory in Diffeology

Local Diffeology, Modeling

Modeling: Manifolds, Orbifolds and Quasifolds

Symplectic Mechanics and Diffeology

Diffeology and Non-Commutative Geometry

Functional Diffeology on Fourier Coefffcients

Smooth Function on Periodic Functions

Symplectic Diffeology on Smooth Periodic Functions

Infinite Torus Action on Smooth Periodic Functions

Basic 1-Forms on Principal Fiber Bundles

Differential of Holonomy for Torus Bundles

Non-symplectic manifold with injective univ. moment map

On Riemannian Metric in Diffeology

A Few Half-Lines

1-Forms on Half-Lines

1-Forms on the Subset Half-Line

Cotangent Space of the Half-Line

1-Forms on Half-Spaces

p-Forms on Half-Spaces

p-Forms on Corners

Differential Forms on the Cross

A note on Hamiltonian Diffeomorphisms

Differential of a Lie-Group Valued Function

The Geodesics of the 2-Torus

The Use of the Moment Map in Geodesic Calculus

The Parasymplectic Space of Geodesics Trajectories

Diffeomorphisms of Geod(T2)

The Diffeomorphisms of the Square

Diffeological Spaces are Locally Connected

Vague Adjunction of a Point to a Space

Embedding a Diffeological Space Into its Powerset

Foliations and Diffeology

Klein Stratiffcation of Diffeological Spaces

Lagrange’s Equations of Motion

Poisson Bracket in Diffeology

Smooth embeddings and smoothly embedded subsets

Seifert Orbifolds

Symplectic spaces without Hamiltonian diffeomorphisms

The Diffeology Framework of General Covariance

Postface: The Beginning of Diffeological Spaces

Appendix: A Categorical Approach to Diffeology

Bibliography