Hyperbolic Surface Subgroups of Doubles

Seminar: 
Geometry & Topology
Event time: 
Tuesday, April 5, 2011 - 12:30pm to Monday, April 4, 2011 - 8:00pm
Location: 
431 DL
Speaker: 
Sam Kim
Speaker affiliation: 
KAIST / Tufts University
Event description: 

Let us consider the presentation complex X of an arbitrary 2-generator presentation. We puncture each 2-cell and double along the holes to get Y, called the double of X. We show that the fundamental group D of Y contains a closed hyperbolic surface group or D splits as a free product (and hence reduces to a simpler case). With more generators, we also resolve the case when the relator set is minimal and k-regular.