Timeline for Asymptotic cone of discrete group of Heisenberg group $\mathbb{H}^3$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 26, 2017 at 17:12 | comment | added | Hee Kwon Lee | @YCor, Ian Agol : Thank you for introducing references. | |
| Mar 24, 2017 at 22:42 | comment | added | YCor | @AntonPetrunin thanks, this was a typo | |
| Mar 24, 2017 at 19:19 | comment | added | Ian Agol | See also mduchin.math.tufts.edu/Current/heis-iumj.pdf | |
| Mar 24, 2017 at 16:43 | history | edited | YCor |
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| Mar 24, 2017 at 16:43 | comment | added | YCor | You have to specify the generating subset, otherwise the asymptotic cone is not defined up to isometry; in particular for $\mathbf{Z}^2$ you implicitly mean the standard generating subset. For Heisenberg, see section 9 in Breuillard's paper "Geometry of groups of polynomial growth and shape of large balls", GGD, math.u-psud.fr/~breuilla/PolGrowth25.pdf. It will be a Finsler metric with respect to some norm on the 2-dimensional tangent plane at 1 of the contact structure, with some polyhedral 1-ball (depending on the choice of generating subset). | |
| Mar 24, 2017 at 16:23 | history | asked | Hee Kwon Lee | CC BY-SA 3.0 |