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UID:a697138ea7c2387c9c15ab07abf4a27a
CATEGORIES:Topology/Geometry Seminar
CREATED:20230920T210921
SUMMARY:Surface Subgroups in Cocompact Kleinian Groups
LOCATION:Hill 705
DESCRIPTION:<p>Kahn and Markovic proved the Surface Subgroup conjecture for closed hype
 rbolic 3-manifolds more than ten years ago. The surface subgroup they const
 ructed can be as close as possible to Fuchsian. However, a closed hyperboli
 c 3-manifold can also have surface subgroups far away from being Fuchsian. 
 Actually, provided any genus-2 quasi-Fuchsian group ? and cocompact Kleinia
 n group G, then for any K&gt;1, we can find a surface subgroup H of G that 
 is K-quasiconformally conjugate to a finite index subgroup F&lt;?. We will 
 point out the difference between my theorem and the&nbsp;original Surface S
 ubgroup Theorem,&nbsp;discuss the proof idea, and introduce some applicatio
 ns. For instance, we can use this theorem to prove that the set of Hausdorf
 f dimensions of limit sets of surface subgroups of G is dense in [1,2].</p>
CONTACT:Zhenghao Rao (Brown)
DTSTAMP:20260826T204157
DTSTART;TZID=America/New_York:20230926T160000
DTEND;TZID=America/New_York:20230926T170000
SEQUENCE:0
TRANSP:OPAQUE
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