Asymptotically conformal and asymptotically rigid mapping class groups

@misc{aramayona2026asymptotically,
  title = {{Asymptotically conformal and asymptotically rigid mapping class groups}},
  author = {Javier Aramayona and George Domat and Christopher Leininger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08849},
  eprint = {2609.08849},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08849},
  note = {CC BY-NC-SA 4.0},
}

TY  - UNPB
TI  - Asymptotically conformal and asymptotically rigid mapping class groups
AU  - Javier Aramayona
AU  - George Domat
AU  - Christopher Leininger
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08849
UR  - https://arxiv.org/abs/2609.08849
AB  - We give conditions ensuring that an asymptotically rigid mapping class group, specifically a surface Houghton group ℋ(S), has finite index in the asymptotically conformal modular group Mod_0(X), where X is a hyperbolic structure on S. These include geometric conditions on the pieces of the underlying rigid structure, as well as the existence in ℋ(S) of an end-periodic homeomorphism which is asymptotically conformal. As a consequence, if S has n≥ 3 ends, then Mod_0(X) has type F_n−1 but not FP_n. We also establish analogous results for L^p modular groups.
ER  -