Moduli spaces of flat Lie algebroid connections

Libor K\v{r}i\v{z}ka

arxiv: 1012.3180 · v1 · pith:VX5YOGXLnew · submitted 2010-12-14 · 🧮 math.DG · math.FA

Moduli spaces of flat Lie algebroid connections

Libor K\v{r}i\v{z}ka This is my paper

classification 🧮 math.DG math.FA

keywords modulispacealgebroidcompactcomplexconnectionsflatmanifold

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We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli space of holomorphic structures on a complex vector bundle over a compact complex manifold.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Lie algebroid Connections, Moduli of $\mathcal{L}$--twisted Principal Objects and motives
math.AG 2026-05 unverdicted novelty 6.0

The work extends non-abelian Hodge theory to transitive Lie algebroids, constructs semiprojective moduli spaces via GIT and Tannakian formalism, and derives a motivic description of their smooth loci in the Grothendieck ring.