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The '''fundamental group''' is a basic construction of [[algebraic topology]].  It associates to any [[topological space]] <math>X</math> a [[group]] <math>\pi_1(X)</math> containing information about the space of "loops" in that space.

The '''fundamental group''' is a basic construction of [[algebraic topology]].  It associates to any [[topological space]] <math>X</math> a [[group]] <math>\pi_1(X)</math> containing information about the structure of the "holes" in the space.  To study the holes, the fundamental group examines the set of loops <math>\gamma : S^1 \to X</math> in the space.

== Simply Connected Spaces ==

== Simply Connected Spaces ==