Editing Polylogarithm (section)

==Monodromy==
The polylogarithm has two [[branch point]]s; one at ''z'' = 1 and another at ''z'' = 0. The second branch point, at ''z'' = 0, is not visible on the main sheet of the polylogarithm; it becomes visible only when the function is [[analytically continued]] to its other sheets. The [[monodromy]] group for the polylogarithm consists of the [[homotopy]] classes of loops that wind around the two branch points. Denoting these two by ''m''<sub>0</sub> and ''m''<sub>1</sub>, the monodromy group has the [[group presentation]]

<math display="block">\langle m_0, m_1 \vert w = m_0 m_1 m^{-1}_0 m^{-1}_1, w m_1 = m_1 w \rangle.</math>

For the special case of the dilogarithm, one also has that ''wm''<sub>0</sub> = ''m''<sub>0</sub>''w'', and the monodromy group becomes the [[Heisenberg group]] (identifying ''m''<sub>0</sub>, ''m''<sub>1</sub> and ''w'' with ''x'', ''y'', ''z'') {{harv|Vepstas|2008}}.