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Jun 11 at 13:58 comment added Son Gohan And what about the question for embedded manifolds in a (possibily compact) oriented manifold $M$, instead of a CW-complex? Are some results available?
Oct 27, 2020 at 18:12 comment added Greg Friedman @AchimKrause I can see why a splitting of $MSO\to H\mathbb{Z}$ would make the homology map surjective, but why does the failure of the splitting imply the failure of homology surjectivity?
Oct 26, 2020 at 14:34 history edited Achim Krause CC BY-SA 4.0
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Oct 26, 2020 at 12:43 history answered Achim Krause CC BY-SA 4.0