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A Greek pi with subscript one, a space and a base point.
Also known as: Fundamental group, Pi one, First homotopy group
The fundamental group records which loops in a space can be shrunk to a point and which cannot, which is how topology detects holes. The base point in the brackets matters for spaces that are not path-connected and is routinely omitted where it does not.
Denotes the fundamental group: homotopy classes of loops at a base point, under concatenation.
Contexts: Mathematics
Detects holes: a space is simply connected exactly when its fundamental group is trivial.
Contexts: Mathematics
Depends on the base point only up to isomorphism within a path component, which is why the base point is usually dropped.
Contexts: Mathematics
A Greek lowercase pi with a small numeral one below right, followed by a bracketed space name and base point.