Watch how analytic continuation around a branch point swaps Riemann sheets — the monodromy group in action.
Complex Plane — Click to place branch points, drag loop
Function & Settings
f(z) = √z: 2 sheets, monodromy σ=(12)
f(z) = log z: ∞ sheets, each loop ↑ branch by 2πi
√(z²−1): branch pts at ±1, fundamental group π₁(ℂ\{±1}) = F₂
Current sheet: 0
Winding around origin: 0
Branch points: 0
Value at z=1: 1.000
After loop value: —
Monodromy: for a multivalued function, encircling a branch point permutes the values (sheets). The monodromy group is the image of π₁(base) → Aut(fiber). For √z: group = ℤ/2ℤ. For log z: group = ℤ.