PreprintCC BY 4.0arXiv
Self measurable embeddings of mapping class groups
Abstract
Given a finite-type orientable surface without boundary, outside of a few low-complexity surfaces, we show that any measurable embedding of the associated mapping class group into itself is a measure equivalence. This is a measure-theoretic analog to the result of Ivanov and McCarthy that mapping class groups are co-Hopfian.
Related
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- Mapping class groups are quasicubical
- On the mapping class groups of simply connected smooth 4-manifolds
- Property Pnaive for non-orientable big Mapping Class Groups
- Ivanov's finite-index Frattini conjecture for subgroups of mapping class groups
BibTeX
@misc{gurieva2026self,
title = {{Self measurable embeddings of mapping class groups}},
author = {Alexandra Gurieva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12054},
eprint = {2610.12054},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12054},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Self measurable embeddings of mapping class groups
AU - Alexandra Gurieva
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.12054
UR - https://arxiv.org/abs/2610.12054
AB - Given a finite-type orientable surface without boundary, outside of a few low-complexity surfaces, we show that any measurable embedding of the associated mapping class group into itself is a measure equivalence. This is a measure-theoretic analog to the result of Ivanov and McCarthy that mapping class groups are co-Hopfian.
ER -