Timeline for Second homology of finitely presented group with free abelianisation
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 6, 2019 at 19:33 | comment | added | Ian Agol | Are you throwing in all such relations? If so, I only count 70 (after throwing out obvious dependent relations). | |
| Feb 6, 2019 at 10:26 | comment | added | FKranhold | Thank you! In fact, I am doing all this in order to see that some $\pi_2(X)$ does not vanish because I believe that $X$ is no $K(G,1)$. ;-) $G$ is of the following form I have generators $a_1,\dotsc,a_5,b_1,\dotsc,b_5,c_1,\dotsc,c5$ and 74 relations which are of the form $[a_i,b_j]=0$ and of the form $b_ic_jb_i^{-1}=b_kc_jb_k^{-1}$ and of the form $a_ib_jc_k=c_kb_ja_i$. My first attempt was to look for relations which are already covered by previous ones, but I did not find one … | |
| Feb 6, 2019 at 4:59 | comment | added | Ian Agol | Deciding if $H_2(G)$=0 is not decidable in general. However, I don't know if this is known for the sort of presentations you are considering. books.google.com/… The issue here is that (I think) one may compute the rank of $H_2(K)$, where $K$ is a 2-complex presenting the group. But one needs to quotient by $\pi_2(K)$, which might not be algorithmic. If one knew more, like solvable word problem or small cancellation, then this might be doable. | |
| Feb 5, 2019 at 23:15 | history | asked | FKranhold | CC BY-SA 4.0 |