Hyperbolic Surface Subgroups of One-ended Doubles of Free Groups
نویسنده
چکیده
Gromov asked whether every one-ended word-hyperbolic group contains a hyperbolic surface group. We prove that every one-ended double of a free group contains a hyperbolic surface group if the free group has rank two, or every generator is used the same number of times in the list of amalgamating words. Our method is based on formulating a stronger conjecture on tilings of closed surfaces combinatorially in terms of Whitehead graphs and proving it for certain classes of graphs.
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تاریخ انتشار 2010