Timeline for Holonomy of compact manifolds
Current License: CC BY-SA 3.0
2 events
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| Apr 11, 2012 at 17:35 | comment | added | Misha | @Claudio: There is an easy (and standard) way to convert your example to a compact one (affine flat structure on the 2-torus). Take a subgroup of $R_+\times SO(2)$ generated by a dilation $A$ and a rotation $B$ of infinite order. Then $A$ and $B$ match opposite edges of a "fundamental membrane" $D$ which is bounded by two concentric circular arcs and two segments contained in lines passing through the origin. Gluing the sides of $D$ via $A$ and $B$ yields a torus with a flat affine structure whose holonomy is nondiscrete (generated by $A$ and $B$). See more in Thurston's Notes or book. | |
| Apr 11, 2012 at 16:46 | history | answered | Claudio Gorodski | CC BY-SA 3.0 |