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Mar 16, 2021 at 12:23 vote accept mathieu
Mar 15, 2021 at 17:48 comment added M.G. @mathieu: Yes, every closed topological manifold is $\mathbb{Z}/2\mathbb{Z}$-orientable. For example, you can find the result and its proof in Hatcher's book, p.235 in 2nd ed.
Mar 15, 2021 at 12:07 comment added mathieu Thank you! I see here that $H_n(M; \mathbb{Z}_2)=\mathbb{Z}_2$.
Mar 15, 2021 at 11:19 history answered Alessandro Codenotti CC BY-SA 4.0