On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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2 results for “quasisections”

Quasisections of circle bundles and Euler classmath.GT

The paper derives a local formula for the Euler number of circle bundles.

problem Calculating the Euler number of circle bundles over surfaces.

method Derives a local formula for the Euler number using quasisections and singularities.

result The Euler number of the bundle equals the sum of weights of singularities of a quasisection.

Euler number circle bundles quasisections singularities Morse bifurcations

2024-10-29abs ↗pdf ↗

A new proof of Milnor-Wood inequalitymath.GT

New proof of Milnor-Wood inequality for circle bundles.

problem Proving the Milnor-Wood inequality for circle bundles.

method Using a local formula to compute the Euler class from the singularities of a quasisection, and sketching two other proofs.

result A new proof of the Milnor-Wood inequality.

Milnor-Wood inequality circle bundles Euler class orientable surfaces genus

2024-12-19abs ↗pdf ↗