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Surface subgroups from linear programming
Duke mathematical journal
We show that certain classes of graphs of free groups contain surface subgroups, including groups with positive b_2 obtained by doubling free groups along collections of subgroups, and groups obtained by "random" ascending HNN extensions of free groups. A special case is the HNN extension associated to the endomorphism of a rank 2 free group sending a to ab and b to ba; this example (and the random examples) answer in the negative well-known questions of Sapir. We further show that the unitdoi:10.1215/00127094-2877511 fatcat:qim6ewgemjcy3dgr5yo5expixe