Keegan J. Flood

collaborators

5 papers

math.CT2026

Canonical differential calculi via functorial geometrization

Keegan J. Flood, Gabriele Lobbia, Giacomo Tendas

Given a category $E$ , we establish sufficient conditions on a faithful isofibration $E \to Mon (V)$ valued in the category of mono…

math.DG2025

Flat extensions of principal connections and the Chern-Simons $3$ -form

Andreas Äap, Keegan J. Flood, Thomas Mettler

We introduce the notion of a flat extension of a connection $I^¸$ on a principal bundle. Roughly speaking, $I^¸$ admits a flat extension if it arises as the pull-back of a component…

math.QA2025

Higher Order Connections in Noncommutative Geometry

Keegan J. Flood, Mauro Mantegazza, Henrik Winther

We prove that, in the setting of noncommutative differential geometry, a system of higher order connections is equivalent to a suitable generalization of the notion of phase space…

math.QA2025

Symbols in Noncommutative Geometry

Keegan J. Flood, Mauro Mantegazza, Henrik Winther

In this paper we prove that the classical Lie bracket of vector fields can be generalized to the noncommutative setting by antisymmetrizing (in a suitable noncommutative sense) the…

math.QA2025

Jet Functors in Noncommutative Geometry

Keegan J. Flood, Mauro Mantegazza, Henrik Winther

In this article we construct three infinite families of endofunctors $J_{d}^{(n)}$ , $J_{d}^{[n]}$ , and $J_{d}^{n}$ on the category of left $A$ -modules, where $A$ is a unital associative al…

Canonical differential calculi via functorial geometrization

Flat extensions of principal connections and the Chern-Simons 3-form

Higher Order Connections in Noncommutative Geometry

Symbols in Noncommutative Geometry

Jet Functors in Noncommutative Geometry

Flat extensions of principal connections and the Chern-Simons $3$ -form