Abelian - Topology and Number Theory

Topology and Number Theory

• Abelian variety, a complex torus that can be embedded into projective space
• Abelian surface, a two-dimensional abelian variety
• Abelian function, a meromorphic function on an abelian variety
• Abelian integral, a function related to the indefinite integral of a differential of the first kind

In category theory

• Pre-abelian category, an additive category that has all kernels and cokernels
• Abelian category, a preabelian category in which every monomorphism is a kernel and every epimorphism is a cokernel

In physics

• A gauge theory is abelian or non-abelian depending on whether its symmetry group is commutative or non-commutative, respectively