Timeline for A natural embedding of the total space of tautological bundle over $G(2,n)$ in $G(2,n+1)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| S Jul 17, 2022 at 0:35 | history | suggested | Samuel Adrian Antz | CC BY-SA 4.0 |
Added \operatorname to Gr.
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| Jul 16, 2022 at 20:39 | review | Suggested edits | |||
| S Jul 17, 2022 at 0:35 | |||||
| Oct 23, 2015 at 17:37 | comment | added | Achim Krause | Alexander-Poincare duality (as in Hatcher, Algebraic Topology, Thm. 3.44) shows that for any embedding of $Gr(k,n)$ into $Gr(k,n+1)$, the cohomology of the complement is related by a long exact sequence to the homology of $Gr(k,n)$ and the cohomology of $Gr(k,n+1)$. This suggests that the topology of the complement is very tightly constrained. To prove that there's no other possible complement is probably very hard, though. Still, this excludes the point and many other spaces essentially simpler than $Gr(k-1,n)$. | |
| Oct 22, 2015 at 21:27 | comment | added | Ali Taghavi | Thank you for very interesting answer. Can one imagine some other embedding which remainder is a compact manifold with a different topological type (different from $Gr(k-1,n)$) | |
| Oct 21, 2015 at 7:57 | history | answered | Achim Krause | CC BY-SA 3.0 |