Timeline for Polynomial growth of the Betti number of balls of the Cayley graphs
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 7, 2013 at 14:14 | history | edited | Lee Mosher |
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| May 4, 2013 at 1:48 | comment | added | Anton Petrunin | @Mark: well, almost equivalent, almost simultaneous :) | |
| May 4, 2013 at 1:18 | comment | added | user6976 | @Anton: My comment is equivalent to your answer. | |
| May 4, 2013 at 1:13 | answer | added | Anton Petrunin | timeline score: 5 | |
| May 4, 2013 at 1:11 | comment | added | user6976 | The property seems to depend on the generating set. Consider the free group $\langle a,b\rangle$ with the generating set $\\{a,b,ab\\}$. The Cayley graph is a tree-graded space where pieces are triangles. A ball of radius $k$ has exponentially many triangles, each contributing 1 to the Betti number. So it seems that the growth is exponential if you use this generating set. Perhaps you should correct the question. | |
| May 4, 2013 at 0:57 | history | asked | Boris Tsygan | CC BY-SA 3.0 |