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Is it true that for even dimensional differentiable manifold $M^{2n}$ all singular homology classes in dimension less than $n$ can be represented by a submanifold?

Joonas Ilmavirta
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user69122
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    Look at the two answers to this duplicate question:http://mathoverflow.net/questions/21171/when-is-a-homology-class-represented-by-a-submanifold – Achim Krause Mar 12 '15 at 00:02
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    In particular, there are obstructions for an integral homology class to be represented by a manifold map altogether (you can get some odd multiple in general), but as soon as that part works you can turn such a map into an embedding in the dimensions you're asking for. – Achim Krause Mar 12 '15 at 00:04

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