Timeline for Relationship between quotient CW-complexes after attaching cells
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 12 at 9:14 | vote | accept | William Thomas | ||
| Apr 12 at 0:52 | answer | added | Allen Hatcher | timeline score: 4 | |
| Apr 11 at 15:45 | comment | added | William Thomas | @FernandoMuro Thanks, I’ll have a look into applying this, was originally trying to prove it inductively on the $n$-skeleton but will try working through this direction. | |
| Apr 11 at 14:30 | comment | added | Fernando Muro | @WilliamThomas I think that Proposition A.2 in the aforementioned book by Hatcher should solve your problem. | |
| Apr 11 at 14:28 | comment | added | William Thomas | @FernandoMuro Thanks for the recommendation. I have checked Hatcher for this and can’t seem to find a statement related to this. However I am trying to use these basic results to get to the bottom of my issue. | |
| Apr 11 at 14:23 | comment | added | William Thomas | @DanRamras to answer you first question the cells we attach to $X$ to get $X’$ are arbitrary and not related to $Y$ in any way, although I appreciate the way I wrote it could have seemed to imply this. | |
| Apr 11 at 14:21 | history | edited | Fernando Muro |
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| Apr 11 at 14:21 | history | edited | William Thomas | CC BY-SA 4.0 |
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| Apr 11 at 14:21 | comment | added | Fernando Muro | I recommend the first appendix of Hatcher's Algebraic Topology book for this kind of general topology issues. | |
| Apr 11 at 14:19 | history | edited | William Thomas | CC BY-SA 4.0 |
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| Apr 11 at 14:15 | comment | added | William Thomas | Apologies for the confusion, will edit the question to make it more clear. The idea is we take $Y$ and then glue in the cells we glued to $X$ (when we made X’) to the subcomplex $X\subset Y$. Whilst doing this we ensure that the new cells glued onto $Y$ only intersect $Y$ at the points of $X\subset Y$ where we define the original gluing. | |
| Apr 11 at 11:21 | comment | added | Dan Ramras | I don’t understand the question. Are the cells you are gluing to X already part of Y? What does “gluing in these same cells to $X\subset Y$ such that they do not intersect $Y$ outside of $X$” mean, precisely? [For those voting to close, could we please give the OP a chance to clarify what he’s asking?] | |
| Apr 11 at 9:31 | history | edited | William Thomas | CC BY-SA 4.0 |
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| Apr 10 at 21:42 | review | Close votes | |||
| Apr 17 at 3:03 | |||||
| Apr 10 at 20:54 | history | asked | William Thomas | CC BY-SA 4.0 |