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  "body": "\n## Summary\n\nMonodromy describes how a multivalued object changes when it is continued around a loop.\nTake a linear differential equation with singular points, and continue a basis of solutions around one of them.\nThe result is a new basis, related to the old one by an invertible matrix.\nThese matrices form a representation of the fundamental group of the plane minus the singular points, the monodromy representation.\nIt is a global invariant of the equation, and it is the subject of [[Hilbert's twenty-first problem|7RHW0KA5RY]].\nSee the [[definition|SK224Y1HNG]] and the related [[monodromy theorem|54QMKJF64A]].\n\n## Explanations\n\n### L1 human\n\nThe function $\\sqrt{z}$ changes sign when one goes once around $0$.\nThe function $\\log z$ gains $2 \\pi i$.\nThese are the simplest cases of monodromy: walking around a singular point and coming back changes the value.\nFor a differential equation, the solutions are mixed among themselves in the same way, and a matrix records the mixing.\n",
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