Timeline for Poincaré dual of the generators of $H^d(\mathbb{RP}^5,\mathbb{Z}_2)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4, 2018 at 14:58 | vote | accept | wonderich | ||
| Sep 4, 2018 at 3:21 | comment | added | Arun Debray | @annieheart the Poincaré dual to $0\in H^k(\mathbb{RP}^n; \mathbb Z/2)$ is an $(n-k)$-dimensional homology class, so a submanifold representing it is an $(n-k)$-dimensional manifold. That's what I meant by "the correct dimension." Since this homology class is zero, it's represented by an $(n-k)$-cycle which is the boundary of some $(n-k+1)$-cycle. For example, you could take an $(n-k)$-dimensional submanifold $N\subset\mathbb{RP}^n$ such that there's an $(n-k+1)$-dimensional submanifold $W\subset\mathbb{RP}^n$ with $N = \partial W$, and one says $N$ bounds. | |
| Sep 4, 2018 at 2:50 | vote | accept | wonderich | ||
| Sep 4, 2018 at 3:13 | |||||
| Sep 4, 2018 at 2:49 | comment | added | annie marie cœur | What is the meaning of "a submanifold of the correct dimension which bounds"??? Thanks... | |
| Sep 3, 2018 at 21:40 | history | answered | Arun Debray | CC BY-SA 4.0 |