Michael Shulman wrote:
what "algebraic" information it uses as input.
> On Sep 24, 2018, at 6:30 PM, Ali Caglayan <alizter@gmail.com> wrote:
>
> However I don't want to discourage you. One possible solution is (differential?) cohesive homotopy type theory (which is at the moment even more undeveloped). This may allow you to talk about manifolds and their structure "synthetically" which would allow for definitions of de Rham cohomology and possibly with care allow you to talk about hilbert schemes of some torus. Pessemistically I would add that it would be at least 10 years before any of this is considered.
just for perspective:
- 10 years ago we had the (higher) homotopy group(oid)s, and not much more.
- 5 years ago the HoTT book was just finished.
- 1 year ago the Serre spectral sequence was finished.
things are moving pretty fast - I would not be so pessimistic.
Steve
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