相关论文: The smooth algebra of a one-dimensional singular f…

These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary…

We construct the holonomy groupoid of any singular foliation. In the regular case this groupoid coincides with the usual holonomy groupoid of Winkelnkemper (1983); the same holds in the singular cases of Bigonnet and Pradines (1985) and…

We introduce the holonomy of a singular leaf $L$ of a singular foliation as a sequence of group morphisms from $\pi_n(L)$ to the $\pi_{n-1}$ of the universal Lie $\infty$-algebroid of the transverse foliation of $L$. We include these…

We consider a class of singular foliations in the sense of Androulidakis and Skandalis that we call transverse order $k$ foliations. These have a finite number of leaves: one hypersurface (the singular leaf) together with the components of…

We introduce singular subalgebroids of an integrable Lie algebroid, extending the notion of Lie subalgebroid by dropping the constant rank requirement. We lay the bases of a Lie theory for singular subalgebroids: we construct the associated…

In this paper we generalize a theorem of M. Hilsum and G. Skandalis stating that the $C^*$- algebra of any foliation of non zero dimension is stable. Precisely, we show that the C*-algebra of a Lie groupoid is stable whenever the groupoid…

The simplest case of a manifold with singularities is a manifold M with boundary, together with an identification of the boundary with a product M1 x P, where P is a fixed manifold. The associated singular space is obtained by collapsing P…

We construct a finite-dimensional higher Lie groupoid integrating a singular foliation $\mathcal{F}$, under the mild assumption that the latter admits a geometric resolution. More precisely, a recursive use of bi-submersions, a tool coming…

This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincar\'e duality…

This paper is concerned with pseudodifferential calculus on manifolds with fibred corners. Following work of Connes, Monthubert, Skandalis and Androulidakis, we associate to every manifold with fibred corners a longitudinally smooth…

This article studies codimension one foliations on projective man-ifolds having a compact leaf (free of singularities). It explores the interplay between Ueda theory (order of flatness of the normal bundle) and the holo-nomy representation…

We show that the convolution algebra of smooth, compactly-supported functions on a Lie groupoid is H-unital in the sense of Wodzicki. We also prove H-unitality of infinite order vanishing ideals associated to invariant, closed subsets of…

Motivated by the study of H\"ormander's sums-of-squares operators and their generalizations, we define the convolution algebra of transverse distributions associated to a singular foliation. We prove that this algebra is represented as…

Looking for the universal covering of the smooth non-commutative torus leads to a curve of associative multiplications on the space $\Cal O_M'(\Bbb R^{2n})\cong \Cal O_C(\Bbb R^{2n})$ of Laurent Schwartz which is smooth in the deformation…

The natural problem we approach in the present paper is to show how the notion of formally smooth (co)algebra inside monoidal categories can substitute that of (co)separable (co)algebra in the study of splitting bialgebra homomorphisms.…

As observed by Kawamata, a $\mathbb{Q}$-Gorenstein smoothing of a Wahl singularity gives rise to a one-parameter flat degeneration of a matrix algebra. A similar result holds for a general smoothing of any two-dimensional cyclic quotient…

We introduce a notion of equivalence for singular foliations - understood as suitable families of vector fields - that preserves their transverse geometry. Associated to every singular foliation there is a holonomy groupoid, by the work of…

For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…

We identify a class of singular algebraic foliations whose leaves through singular points retain regularity. The proof consists in showing existence of residual gerbes for certain formal stacks, which do not enjoy smooth presentations. As…

We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…