Free Group Action

A Group Action : G × X X \cdot:G\times X\to X is fixed-point free (or simply free) if g x = x 𝑔 𝑥 𝑥 g\cdot x=x for some x : X : 𝑥 𝑋 x:X implies that g = ε 𝑔 𝜀 g=\varepsilon . Equivalently, a group action is free if the Shear Map is a Monomorphism.