PreprintCC BY 4.0arXiv
Surface subgroups of Baumslag doubles along short words
Abstract
If U is a minimal, diskbusting, finite list of words in a free group Fn 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 Fn along U virtually contains a π1-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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BibTeX
@misc{xuan2026surface,
title = {{Surface subgroups of Baumslag doubles along short words}},
author = {Hoang Le Xuan and Nam Hung Tran Nguyen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21191},
eprint = {2609.21191},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21191},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Surface subgroups of Baumslag doubles along short words
AU - Hoang Le Xuan
AU - Nam Hung Tran Nguyen
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.21191
UR - https://arxiv.org/abs/2609.21191
AB - 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.
ER -