Timeline for Lurie's applications of $\infty$-topoi in topology
Current License: CC BY-SA 4.0
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| Feb 7, 2022 at 0:49 | comment | added | David Roberts♦ | It's probably more in shape theory, which deals with the algebraic topology of spaces for which the usual invariants like homotopy groups and singular cohomology fail to detect nontrivial topology. If a topological space is so bad that there are no non-constant maps from standard simplices, then singular cohomology is trivial. Similarly if the topology is "too global" to detect with maps from boundaries of simplices (eg the Warsaw circle). | |
| Feb 6, 2022 at 21:07 | comment | added | Will Sawin | étale cohomology isn't much useful in topology - more in algebraic geometry. So a list of applications in topology wouldn't necessarily include generalizations of étale cohomology. | |
| Feb 6, 2022 at 20:57 | history | asked | user1022117 | CC BY-SA 4.0 |