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arxiv:2609.21191
Surface subgroups of Baumslag doubles along short words
Published on Sep 18
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Abstract
If U is a minimal, diskbusting, finite list of words in a free group F_n of rank n such that the sum of the lengths of words in U is at most 2n+4, we prove that the natural presentation complex of the Baumslag double of F_n along U virtually contains a π_1-injective embedded closed hyperbolic surface. This verifies the Tiling Conjecture of Kim and Wilton for this type of lists of words, and in particular, implies that the corresponding Baumslag double contains a hyperbolic surface subgroup.
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