Monodromy
（重定向自Monodromic group）
![The imaginary part of the complex logarithm. Trying to define the complex logarithm on C \ 0 gives different answers along different paths. This leads to an infinite cyclic monodromy group and a covering of C \ 0 by a helicoid (an example of a Riemann surface).](/Images/godic/202501/28/Imaginary_log_analytic_continuation1225.png")
In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they 'run round' a singularity. As the name implies, the fundamental meaning of monodromy comes from 'running round singly'. It is closely associated with covering maps and their degeneration into ramification; the aspect giving rise to monodromy phenomena is that certain functions we may wish to define fail to be single-valued as we 'run round' a path encircling a singularity. The failure of monodromy is best measured by defining a monodromy group: a group of transformations acting on the data that encodes what does happen as we 'run round'.