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SUMMARY:Thar she blows - in pursuit of a classification of finite index su
 bgroups of SL_2(Z) in terms of wallpaper groups - Marj Batchelor
DTSTART:20121019T130000Z
DTEND:20121019T140000Z
UID:TALK41144@talks.cam.ac.uk
CONTACT:Jonathan Nelson
DESCRIPTION:There is an equivariant map from the upper half plane (with SL
 _2(Z) acting by mobius transformations) to the complex plane (with the act
 ion of a subgroup affine transformations which preserve a triangular latti
 ce).  The homomorphism from SL_2(Z) onto this group of affine transformati
 ons provides an obvious source of finite index subgroups of SL_2(Z). The c
 onjecture is that finite index subgroups are all "lifts" of subgroups of t
 he translation subgroup. I will describe why the equivariant map is plausi
 ble\, and talk about the kernel of the homorphism and the lifts of transla
 tion groups.
LOCATION:MR4
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