A new proof of Milnor-Wood inequality
Geometric Topology
2025-12-04 v5
Abstract
The Milnor-Wood inequality states that if a (topological) oriented circle bundle over an orientable surface of genus has a smooth transverse foliation, then the Euler class of the bundle satisfies We give a new proof of the inequality based on a (previously proven by the authors) local formula which computes from the singularities of a quasisection. We also sketch two other proofs: one based on Poincar\`{e} rotation number theory, and the other of topological nature.
Keywords
Cite
@article{arxiv.2412.14553,
title = {A new proof of Milnor-Wood inequality},
author = {Gaiane Panina and Timur Shamazov and Maksim Turevskii},
journal= {arXiv preprint arXiv:2412.14553},
year = {2025}
}