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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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3 results for “PB-groupoids”

Principal bundle groupoids, their gauge group and their nervemath.DG

The paper generalizes bundle gerbes over groupoids and their correspondence with PB groupoids.

problem Generalizing bundle gerbes over groupoids and their properties.

method Developed a functorial correspondence between PB groupoids and bundle gerbes over groupoids.

result Built a correspondence between PB groupoids and bundle gerbes over groupoids, including partial quotients.

groupoids bundle gerbes principal bundles functorial correspondence nerve

2021-08-16abs ↗pdf ↗

PB-groupoids vs VB-groupoidsmath.DG

Paper defines PB-groupoids and their relation to VB-groupoids.

problem Establishing PB-groupoids as a Lie 2-groupoid counterpart.

method Defining PB-groupoids as Lie 2-groupoid actions on diagrams of Lie groupoids and principal bundles.

result PB-groupoids generalize VB-groupoids and provide a new correspondence between them and principal bundles.

PB-groupoids VB-groupoids Lie 2-groupoids principal bundles vector bundles

2024-06-10abs ↗pdf ↗

Fat Lie Theorymath.DG

Introduces fat Lie theory for Lie groupoids and algebroids.

problem Representation theory of Lie groupoids and algebroids.

method Introduces fat extensions and abstract 2-term representations up to homotopy (ruths). Establishes correspondences and equivalences.

result One-to-one correspondence between fat extensions and abstract 2-term representations up to homotopy.

fat Lie theory Lie groupoids algebroids representations homotopy

2026-03-09abs ↗pdf ↗