Timeline for Acyclic group and finite CW-complex
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 6, 2020 at 14:11 | comment | added | HJRW | @AndréHenriques -- that would be a great thing to do, but unfortunately I don't have time. If you click through to the wikipedia page, you'll see that small-cancellation conditions are quite explicit, and easy to fulfill, as Rylee's example shows. Someone who's genuinely interested in answering the question won't have any difficulty building an infinite family of examples of presentations using this recipe (though it is a little trickier to show that you get infinitely many different isomorphism types). | |
| Feb 6, 2020 at 3:39 | comment | added | Robbie Lyman | @AndréHenriques Sure, take $F_2 = \langle a,b\rangle$. A suitable pair of elements is $a(aba^{-1}b^{-1})^5$ and $b^6a^2b^3a^{-1}b^{-8}a^{-1}$. I believe the longest common piece is $a^2b$, and $3$ is less than one sixth of the length of each word, which is cyclically reduced. Counting exponent sums, we see that they generate the abelianization. | |
| Feb 5, 2020 at 22:24 | comment | added | André Henriques | If explicit examples are easy to construct, it might be worth constructing some explicit examples for the interested readers. | |
| Feb 5, 2020 at 21:57 | history | answered | HJRW | CC BY-SA 4.0 |