Timeline for Amalgamated product acting on CAT(0) cube complex
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 10, 2023 at 10:33 | comment | added | HJRW | There's nothing extra to check for HNN extensions: as long as both attaching maps are local isometries, the resulting graph of spaces satisfies the link condition, hence is non-positively curved and cannot contain Baumslag--Solitar subgroups. Note that, in the natural model for $BS(1,2)$, you can't simultaneously make both attaching maps local isometries. | |
| Nov 10, 2023 at 9:19 | comment | added | HenrikRüping | I would have a look at Chapter II.11 Gluing Constructions in Bridson-Haefliger. II.11.1 should do the job, but a better reference for this construction would be II.11.18. | |
| Nov 10, 2023 at 8:55 | comment | added | bishop1989 | Yes, it is isometric embedding, I have edited the question. Your idea is something like if I am not wrong, you considered $Y \times [0,1]$ and glued both ends to $X_i$'s (just like mapping cylinder) and translate the copies of $Y\times [0,1]$ and repeat the procedure. I was not confident enough! Thanks a lot. Can you provide a reference to gluing lemma for CAT(0) cube complexes you mentioned above? | |
| Nov 10, 2023 at 8:16 | history | edited | HenrikRüping | CC BY-SA 4.0 |
Typo and one additional outlook-paragraph
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| Nov 10, 2023 at 8:01 | history | answered | HenrikRüping | CC BY-SA 4.0 |