Let \(X\) and \(Y\) be topological spaces. A continuous map \(f\colon X\to Y\) is nullhomotopic if it is homotopic to a constant map: there are \(y_0\in Y\) and a continuous map \(F\colon X\times[0,1]\to Y\) with \(F(x, 0) = f(x)\) and \(F(x, 1) = y_0\) for all \(x\in X\).
If \(f\colon X\to Y\) is nullhomotopic, then \(f_*\colon\tilde H_n(X)\to\tilde H_n(Y)\) is zero for every \(n\).
See [@Hat02].