Title    name   Topology Seminar Hyperbolic Surface Subgroups of One-Ended Doubles of Free Groups Kim, Sanghyun (KAIST and Tufts University) 2010-12-23   The polygonality in free groups concerns the existence of a van Kampen diagram on a closed surface with certain restrictions. By formulating polygonality in terms of corresponding Whitehead graphs, we prove that the double of a rank-two free group is one-ended if and only if it contains a hyperbolic surface group. For the free groups of higher ranks, we resolve the case when the amalgamating list of words have a regular Whitehead graph; a key ingredient is Edmonds and Seymour's characterizations of perfect matching polytopes. This is partially joint work with Sang-il Oum and with Henry Wilton.

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