synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
identity type, equivalence of types, definitional isomorphism
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
Examples.
The Euler-Arnold equation governs Hamiltonian dynamics on Lie groups.
The original influential is
A survey is in
Terence Tao, The Euler-Arnold equation (web)
Hernan Cendra, Jerrold Marsden, Sergey Pekarsky, Tudor Ratiu, Variational principles for Lie-Poisson and Hamiltonpincaré equations_ (pdf)
Last revised on September 18, 2012 at 00:15:16. See the history of this page for a list of all contributions to it.