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PreprintarXiv licencearXiv

An explicit section of the Laudenbach-type exact sequence of the big mapping class group of MΓ

  • Jorge Andres Robinson Arrieta
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Abstract

Given a locally finite graph Γ, Udall proved that the mapping class group of the doubled handlebody associated to Γ is an extension of the mapping class group of Γ by a possibly infinite direct product of ℤ2, and that this extension splits. We give a formula for Udall's section restricted to the pure mapping class group and, when Γ has finitely many ends, on the whole mapping class group.

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Cite

BibTeXRIS
BibTeX
@misc{arrieta2026explicit,
  title = {{An explicit section of the Laudenbach-type exact sequence of the big mapping class group of $M_Γ$}},
  author = {Jorge Andres Robinson Arrieta},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24912},
  eprint = {2610.24912},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24912},
}
RIS
TY  - UNPB
TI  - An explicit section of the Laudenbach-type exact sequence of the big mapping class group of M_Γ
AU  - Jorge Andres Robinson Arrieta
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24912
UR  - https://arxiv.org/abs/2610.24912
AB  - Given a locally finite graph Γ, Udall proved that the mapping class group of the doubled handlebody associated to Γ is an extension of the mapping class group of Γ by a possibly infinite direct product of ℤ_2, and that this extension splits. We give a formula for Udall's section restricted to the pure mapping class group and, when Γ has finitely many ends, on the whole mapping class group.
ER  -