Timeline for Bordism for oriented triangulable manifolds without smooth differentiable structures
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 17, 2023 at 11:19 | answer | added | Claus | timeline score: 11 | |
| Dec 8, 2021 at 17:58 | comment | added | Connor Malin | The paper "Classification of simplicial triangulations of topological manifolds" of Galewski and Stern relates triangulations to lifts of the microtangent bundle to a space $\operatorname{BTri}$. If there is a positive answer to your question, presumably the homology theory is represented by some $\operatorname{MTri}$. | |
| Dec 8, 2021 at 17:34 | comment | added | Tom Goodwillie | $w_j(TM)$ does not require a triangulation (a $PL$ structure). The tangent microbundle of a topological manifold has Stiefel-Whitney classes. In fact, even a (stable) spherical fibration on a space X has SW classes; $w_j$ can be defined as the class that corresponds via the Thom isomorphism to $Sq^j$ of the Thom class. | |
| Dec 8, 2021 at 17:10 | comment | added | Ryan Budney | I don't understand what category of manifold you are interested in. Are you talking about the image of the forgetful map $PL \to TOP$? | |
| Dec 8, 2021 at 17:04 | history | asked | wonderich | CC BY-SA 4.0 |