| 释义 |
fundamental group A topological invariant important in algebraic topology and the first of the homotopy groups. For a path-connected space X with base point x0, the fundamental group π1(X) is the set of equivalence classes of continuous loops γ:[0,1]→X such that γ(0)=γ(1) = x0, and where two loops are equivalent if they are homotopic. The product γ1⁎γ2 of two loops is the loop γ2 followed by γ1 and the inverse of γ is the loop in reverse. A continuous function f:X→Y induces a homomorphism f⁎:π1(X)→π1(Y) by sending γ to f(γ). The circle's fundamental group is ℤ; the knot group of a knot is the fundamental group of its complement.
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