TeXipedia

curvearrowright

Represents a curved arrow pointing rightward, commonly used to denote cyclic operations or rotational transformations.

Overview

Particularly useful in advanced mathematics and theoretical physics for indicating cyclic group actions, rotations, or sequential transformations.

  • Frequently appears in group theory to denote group actions on sets
  • Used in topology and abstract algebra to represent mappings or transformations
  • Common in dynamical systems to indicate cyclic or periodic behavior
  • Serves as a more elegant alternative to straight arrows when depicting circular or cyclic relationships

Examples

Showing a cyclic group operation on elements.

G↷XG \curvearrowright X 
G \curvearrowright X

Indicating a right group action in abstract algebra.

(g1g2)↷x=g1↷(g2↷x)(g_1g_2) \curvearrowright x = g_1 \curvearrowright (g_2 \curvearrowright x) 
(g_1g_2) \curvearrowright x = g_1 \curvearrowright (g_2 \curvearrowright x)

Representing a rotation operation in geometry.

R↷R2R \curvearrowright \mathbb{R}^2 
R \curvearrowright \mathbb{R}^2