Timeline for If two smooth manifolds are homeomorphic, then their stable tangent bundles are vector bundle isomorphic
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| Aug 7, 2020 at 13:52 | comment | added | Jens Reinhold | I am not sure what exactly Novikov proved originally, but I think these extra conditions are not necessary for the statement to hold. I suggest having a look at the "epilogue" of Milnor-Stasheff, which explicity mentions Novikov's result. There are also other proofs using different methods: arxiv.org/pdf/0901.0819.pdf | |
| Aug 7, 2020 at 10:24 | history | edited | Jens Reinhold | CC BY-SA 4.0 |
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| Aug 7, 2020 at 10:15 | comment | added | Michael Albanese | I was under the impression that Novikov proved that the rational Pontryagin classes are homeomorphism invariants of a closed, orientable, smooth manifold. Can the closedness and orientability hypotheses be removed? It should be noted that the non-zero Pontryagin class I refer to in my answer is torsion. | |
| Aug 7, 2020 at 7:04 | history | answered | Jens Reinhold | CC BY-SA 4.0 |