Timeline for An explicit example of a finitely presented group containing a subgroup isomorphic to $(\mathbb Q,+)$.
Current License: CC BY-SA 4.0
6 events
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| Jun 25, 2020 at 7:58 | comment | added | YCor | @MicheleTriestino Thanks! that proposition states that for every rational mod $\mathbf{Z}$ is rotation number of some element of $T$, and the proof starts, for every $n$, exhibiting an element $g_n$ of order $n+2$ (explicit: $0\mapsto 1-2^{-n-1}$, $1/2\mapsto 1$, $1-2^{-n-1}\mapsto 1-2^{-n}$, affine in between). They credit anonymous handwritten notes for $g_n$. | |
| Jun 25, 2020 at 7:47 | comment | added | user47274 | I have just realized that the proof of Proposition III.2.1 of Ghys-Sergiescu eudml.org/doc/140083 contains a construction of torsion elements of every order in $T$ | |
| May 14, 2020 at 8:20 | comment | added | YCor | @MicheleTriestino it's obvious modulo having this observation in mind. Once you have an explicit element of order 3, it's obvious that it exists, and actually the whole recpe to produce elements of arbitrary odd order is very elementary... Anyway this last sentence was a bit meta-mathematical: I meant that I didn't have the right picture in mind. Nevertheless your observation might give the oldest reference for this observation that there are nontrivial elements of odd order in $T$. | |
| May 14, 2020 at 8:05 | comment | added | user47274 | It is quite obvious that $T$ has elements of order 3, since $T$ contains $\mathrm{PSL}(2,\mathbb{Z})$ (this follows from Thurston's realization of $T$ as a group of piecewise $\mathrm{PSL}(2,\mathbb{Z}$ homeomorphisms). The first non-trivial case is order 5... | |
| May 7, 2020 at 21:52 | history | edited | YCor | CC BY-SA 4.0 |
shrinked paragraph about unpublished result
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| May 7, 2020 at 8:33 | history | answered | YCor | CC BY-SA 4.0 |