Are Chern classes topological invariants? To be more precise: Given two complex manifolds $M$ and $N$.
Does a homeomophism $f:M\to N$ map Chern classes to Chern classes?
2026-03-25 19:16:09.1774466169
Topological invariance of chern classes
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No. Even Chern numbers are not topologically invariant — an example was given by Borel and Hirzebruch in 1959 (Characteristic classes and homogeneous spaces, §24.11).