22 problems

Let a Lie groupoid be effective when the only isotropic arrows that have trivial infinitesimal effect are the identities. A Lie groupoid is proper when its source–target map is pro…

Almost action conjecture. If $\sigma:G\to H$ is a map such that

Proper groupoid structure conjecture. If $x$ is a fixed point of a proper groupoid $\Gamma$, then $x$ has an invariant neighborhood on which $\Gamma$ is isomorphic to the action gr…

Compatibility conjecture. The first two methods produce the same $Q$-algebroid and, although the third method produces a different $Q$-algebroid, it results in the same double comp…

Weinstein's conjecture. This topological groupoid has some differentiable structure.

Let $A$ be a Lie algebroid that admits a proper integrating groupoid $\mathcal{G}$ whose $s$-fibers are $2$-simply connected. Cohomological rigidity conjecture. Then … This conject…

Conjecture. Under these assumptions, there exists a $(\Gamma,R)$-twisted vector bundle.

Lie-groupoid van Est conjecture. The map

Natural-isomorphism invariance conjecture. The natural isomorphism induces an isomorphism

Double-groupoid van Est conjecture. There is a van Est map from the cohomology of the double Lie groupoid to the cohomology of its LA-groupoid. If differentiation takes place in th…

Let $G\rightrightarrows M$ be a proper Lie groupoid. If $G\rightrightarrows M$ is invariantly linearizable, then it admits a complete $0$-metric $\eta_0$. Conversely, the converse…

Ammann–Lauter–Nistor's conjecture. The injectivity radius of a connected manifold with Lie structure at infinity is positive.

Hausdorff symplectic realization conjecture. Every Hausdorff symplectic complete realization gives rise to a Hausdorff symplectic groupoid.

Conical-singularity conjecture. The zero locus of the momentum section has only conical singularities.

Let $\mathcal{G}$ be a proper étale Lie groupoid modelled on an infinite-dimensional space; such a groupoid is called an orbifold groupoid. An orbifold in local charts is a corresp…

Let $\mathcal{G}\rightrightarrows M$ be a Lie groupoid, and let $\mathrm{Vect}(\mathcal{G})$ denote its category of multiplicative vector fields. Hepworth's conjecture. The categor…

The paper considers pseudoactions and their morphisms, with Theorems … providing versions of Lie I and Lie II for pseudoactions under the hypotheses established there. General-morp…

Let $G\rightrightarrows M$ be an $s$-locally trivial proper Lie groupoid. Invariant linearization around a saturated embedded manifold means that a neighborhood of the subgroupoid…

Weighted-category conjecture. The weighted category of an orbifold groupoid coincides with the unweighted category of its inertia groupoid:

Global faithfulness conjecture. The groupoid ${\mathcal G}$ is Morita equivalent to the translation groupoid associated with an action of some compact Lie group; equivalently,…

Tannaka duality conjecture. The groupoid ${\mathcal T^{\infty}({\mathcal G})}$ is a Lie groupoid for every proper Lie groupoid ${\mathcal G}$, without assuming regularity.

Representability conjecture. All orbifolds are representable by translation groupoids $G \ltimes M$.