Timeline for Continuity of Alexander-Spanier cohomology
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 22, 2016 at 8:22 | answer | added | Matthias Wendt | timeline score: 4 | |
| Dec 21, 2016 at 19:58 | comment | added | Matthias Wendt | My comment on continuity of Cech cohomology was a bit hasty. The classical sources only do this for compact spaces. However, there is a weak continuity for paracompact spaces by results of Lee and Raymond. I'll search a bit more through the literature and then come back to give more details. | |
| Dec 21, 2016 at 14:11 | comment | added | Mehmet Onat | @MatthiasWendt Is it true that Cech cohomology on paracompact spaces has the continuity property? | |
| Dec 21, 2016 at 14:09 | comment | added | Mehmet Onat | @MatthiasWendt Actually i want to know that if $G$ is a compact totally disconnected group acting on a paracompact space X, then the orbit map $X\rightarrow X/G$ induces isomorphism (or monomorphism) on Alexander-spanier cohomology with closed supports? | |
| Dec 21, 2016 at 14:04 | comment | added | Mehmet Onat | @MatthiasWendt I know only that the continuity holds for Alexander-Spanier cohomology with compact supports on locally compact spaces. You can look at Bredon's Sheaf Theory book (14.6. Corollary page 103). I dont know that it holds on Alexander-Spanier cohomology with closed support on paracompact spaces. | |
| Dec 20, 2016 at 13:13 | comment | added | Matthias Wendt | Do you mean closed support or compact support? (Every function on a topological space has closed support by definition.) You probably are aware of the fact that continuity holds for Alexander-Spanier cohomology (no support condition) on paracompact spaces, by identification with Cech cohomology (via sheaf cohomology). This is discussed in Spanier's "Algebraic topology". | |
| Dec 19, 2016 at 16:58 | history | edited | Mehmet Onat | CC BY-SA 3.0 |
deleted 5 characters in body; edited tags
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| Dec 19, 2016 at 14:51 | history | asked | Mehmet Onat | CC BY-SA 3.0 |