= Mod-two degree of a map between closed manifolds
{title2=$\deg_2(f)\in\mathbb F_2$}
For a map $f:M\to N$ between closed connected $n$-manifolds, the mod-two degree is defined by $f_*[M]_2=\deg_2(f)[N]_2$. Every manifold has a mod-two orientation class, so no orientability assumption is needed. It is invariant under <homotopy>. A nonsurjective map has mod-two degree zero: mapping the fundamental classes into the local relative homology at a missed target point makes the source contribution zero but leaves the target local generator nonzero.
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