A new proof of Milnor-Wood inequality
Abstract
The Milnor-Wood inequality states that if a (topological) oriented circle bundle over an orientable surface of genus g has a smooth transverse foliation, then the Euler class of the bundle satisfies |E|≤ 2g-2. We give a new proof of the inequality based on a (previously proven by the authors) local formula which computes E 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.
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