PreprintarXiv licencearXiv
Codimension-one holomorphic Anosov diffeomorphisms
Abstract
We prove that every codimension-one holomorphic Anosov diffeomorphism of a compact connected complex manifold is biholomorphically conjugate to a hyperbolic automorphism of a complex torus. This verifies a conjecture of Ghys in the codimension-one case and, in particular, in complex dimension three.
Related
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- Unstable entropy for Anosov diffeomorphisms on tori isotopic to Anosov linear maps
- On the Absence of Anosov Factors for DA Local Diffeomorphisms
- Topological Expansivity and Shadowing for Anosov Diffeomorphisms
- Anosov Diffeomorphisms of Finite-Type Surfaces
BibTeX
@misc{zhang2026codimensionone,
title = {{Codimension-one holomorphic Anosov diffeomorphisms}},
author = {Jiesong Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.37695},
eprint = {2609.37695},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37695},
}
RIS
TY - UNPB
TI - Codimension-one holomorphic Anosov diffeomorphisms
AU - Jiesong Zhang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.37695
UR - https://arxiv.org/abs/2609.37695
AB - We prove that every codimension-one holomorphic Anosov diffeomorphism of a compact connected complex manifold is biholomorphically conjugate to a hyperbolic automorphism of a complex torus. This verifies a conjecture of Ghys in the codimension-one case and, in particular, in complex dimension three.
ER -