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  "body": "\n## Summary\n\nThe fundamental group $\\pi_1(X, x_0)$ of a [[pointed space|T9DG8DDE75]] is the [[group|G5S1M9]] of loops at $x_0$ up to [[path homotopy|CCNKA8C711]], with concatenation of loops as product.\nIt is the first invariant of algebraic topology that detects one-dimensional holes.\nHomotopy equivalent path-connected spaces have isomorphic fundamental groups.\nFor example, the plane has trivial fundamental group, while the [[circle|060W5CBZP6]] has fundamental group $\\Z$.\n\n## Explanations\n\n### L1 human\n\nStand at a point of a space and walk along loops that come back to where you started.\nTwo loops count as the same if one can be deformed into the other while the start stays fixed.\nDoing one loop after another is the product.\nOn a circle, a loop is classified by how many times it goes around, counted with sign, so the group is the integers.\n",
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