Definition

Fundamental Group

Algebraic Topology · algebraic-topology.tex

Loops Homotopy Homotopy Equivalence Class Let $f$ be a loop. Let $[f]$ denote the equivalence class under homotopy for $f$. We define $\pi_1(X,x)$ to be the set of equivalence classes of loops that start and end at $x$. We will show that this is a group. This is the fundamental group of $X$.

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