I would like an example of a map $f: M \to N$ between closed oriented connected $n$-manifolds (the smaller the $n$ the better!) such math $\operatorname{deg}(f) = 0$ but $f$ is not nullhomotopic.
2026-03-30 00:18:09.1774829889
Nonnullhomotopic degree 0 map
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$$S^1 \times S^1 \xrightarrow{\pi_1} S^1 \cong S^1 \times \{1\} \hookrightarrow S^1 \times S^1$$