Timeline for A manifold is a homotopy type and _what_ extra structure?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 22, 2017 at 15:06 | answer | added | Manuel Bärenz | timeline score: 23 | |
| Aug 22, 2017 at 13:23 | vote | accept | Manuel Bärenz | ||
| Aug 17, 2017 at 7:33 | comment | added | Andrew Ranicki | The discussion in https://mathoverflow.net/questions/129/how-can-you-tell-if-a-space-is-homotopy-equivalent-to-a-manifold is relevant. | |
| Aug 16, 2017 at 18:04 | answer | added | Igor Rivin | timeline score: 22 | |
| Aug 16, 2017 at 17:48 | comment | added | Paul Siegel | In higher dimensions there for sure other obstructions, and indeed these are the primary objects of study in surgery theory (as Mark Grant pointed out). One of the main ideas is that manifolds have tangent spaces and tangent spaces have unit spheres, so a manifold is necessarily the base space of a certain kind of spherical fibration. This idea together with Poincare duality eventually leads to necessary and sufficient conditions for a homotopy class to contain a manifold. (Due to Browder, Novikov, Sullivan, and Wall in the 60's i think.) | |
| Aug 16, 2017 at 17:44 | comment | added | Hugh Thomas | You seem to be writing homology with upper indices and cohomology with lower indices. Or am I confused? | |
| Aug 16, 2017 at 17:21 | comment | added | Mark Grant | I suspect the answer to all your questions might be: surgery theory. But I'll leave it to the experts to comment furher :) | |
| Aug 16, 2017 at 17:15 | history | asked | Manuel Bärenz | CC BY-SA 3.0 |