Group actions

operation of the elements of a group as transformations or automorphisms (mathematics)

subset of a space acted upon by a group, which contains exactly one point from each of the orbits

fiber bundle whose fibers are group torsors (groups with the identity element forgotten)

topological space consisting of equivalence classes of points in another topological space

alt=Hyperbolic symmetry comparison to Euclidean symmetry|thumb|23star Orbifold Example In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space that is locally a finite group quotient of a Euclidean space.

symmetry-based invariance to continuous group action

mathematical formalization of the motion of particles in a fluid

concept in mathematics regarding sets operating on groups

tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action, generalizing the classical notions of linear and angular momentum

Maps whose domain and codomain are acted on by the same group, and the function commutes

set of points linked through the evolution function of a dynamical system